Financial Algebra Advanced Algebra with Financial Applications 2e Robert Gerver Richard J Sgroi Instant Download - Complete Test Bank With Answers Sample Questions Are Posted Below 1. Employers are usually charged a flat fee to place classified ads in the newspaper. a. True b. False ANSWER: False RATIONALE: Employers …
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Financial Algebra Advanced Algebra with Financial Applications 2e Robert Gerver Richard J Sgroi
Instant Download – Complete Test Bank With Answers
Sample Questions Are Posted Below
1. Employers are usually charged a flat fee to place classified ads in the newspaper.
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2. Social Security tax is paid on all your income, whereas Medicare tax is paid up to the maximum taxable income amount.
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| 3. Blinko’s charges $24.99 to print 100 top-quality, single-page résumés. Each additional 50 copies cost $10. This cost, r(x), written as a piecewise function, is:
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4. The purpose of worker’s compensation is to offer benefits to eligible employees that have become unemployed.
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5. Bruce is paid semimonthly, so he receives 24 paychecks a year.
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6. McKenzie sells textbooks. She receives 7% on her first $1,000 in sales and 15% on the balance of her sales. If her sales in one month were $14,500, she would earn $2,025 in commission.
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7. Jim was offered a job as a computer programmer making $65,000 per year. Another company offered Jim a position earning $1,200 a week. The job with the $65,000 salary pays more.
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8. Royalty is a percentage paid on the money earned from sales on items such as tickets, books, artwork, and music CDs.
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9. Cherie accepted a job through an employment agency. The job pays $1,100 a week. The agency charges 30% of her first 4 weeks, pay. To find the amount she owes the agency, she should multiply her first four weeks’ salary by 0.03.
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10. This spreadsheet calculates a yearly pension. The formulas are entered in column B. What is the spreadsheet formula for B7?
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11. In 2008, Yolanda paid $3,875 in Social Security tax. If the Social Security tax rate was 6.2% to the maximum income of $94,200 that year, what was Yolanda’s taxable income?
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12. What is Medicare?
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13. In 2005, Lee began working as a nurse anesthetist with a taxable income of $119,000. The Medicare tax was 1.45% and the Social Security tax rate was 6.2% to the maximum income of $90,000 that year. How much did Lee pay in FICA taxes in 2005?
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14. Catalina works part-time at a bakery earning $7.50 an hour. In the past five days, her time card shows that she worked 3.3, 2.9, 4.0, 3.5, and 2.1 hours. What is her gross pay for the five days?
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15. Miquel pays $47 semimonthly for health insurance which is 15% of the total cost. His employer pays the rest. What is the total yearly cost to the nearest dollar of Miquel’s health insurance?
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16. This piecewise function represents the Social Security taxes for 2009. How much did Rachel pay in Social Security tax if she earned $102,000 in 2009?
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17. Federal and state laws provide rules on the lowest hourly rate that can be paid to a worker in the United States. What is that rate called?
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18. Pimmi gets paid $0.50 for the first 100 craft kits that she assembles. She earns $0.75 for each kit over 100. This week she assembled 135 kits. How much did she earn?
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19. Michelle receives $32,000 per year as an assistant fast food manager. Her benefits include health insurance, paid holidays, retirement contributions, and a two-week paid vacation each year. Because she wears a uniform, Michelle calculates that she saves $2,500 on clothing costs per year. She constructed this table to show the value of each benefit. What is her annual salary, including benefits?
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20. Marcus earned $54,000 last year when the Social Security tax was 6.2% of income up to $94,200. His Medicare tax was 1.45%. How much did he pay in Social Security and Medicare taxes last year?
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21. Maryanne began a job that gives her 3 days of vacation each year she is employed, up to a maximum of 24 days of vacation time. How many years will she be at the company when she reaches the maximum amount of vacation time?
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22. Mrs. Brown has been working in a factory for 28 years. She is preparing to retire. Her pension is calculated on the average of her last 3 years’ salaries, when she earned $38,592; $37,590; and $37,010. Her employer will give her 1.8% of that average for each year she worked. Calculate her pension.
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23. Juanita gets paid for every apron she embroiders. Last week, she earned $185. If she earns $2.50 for each embroidered piece, how many aprons did she embroider last week?
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24. A local newspaper charges $18 for the first three lines of a want ad, and then $6.50 for each additional line. Express the cost of an x-line ad, c(x), as a piecewise function.
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25. Singh works at a restaurant where he is paid by the hour plus time and a half for his hours over 40. Last week, he worked 3 hours overtime, and his gross pay was $380.48. What is his hourly wage?
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26. If Leona receives her paycheck biweekly, how many checks does she receive in a year?
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27. Nancy was laid off and applied for unemployment benefits in July. In her state, the weekly unemployment benefit is 55% of the 26-week average of the two highest-salaried quarters of the year leading to her application. In April, May, and June, Nancy earned a total of $13,500. In January, February, and March, her total income was $12,775. What will Nancy’s weekly benefits be?
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28. Katelyn sells cars at a used-car dealer on commission. The car lot pays an 18% commission when the profit on a car is under $400, 22% when the profit is at least $400 and less than $1,000, and 24% when the profit is $1,000 or more. Write a piecewise function to represent the commission, c(x) as a function of the profit, x.
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29. Emily wants to have her résumé printed. The printing company charges $24.50 for the first 100 résumés, and then a flat rate for each additional 100 résumés. Emily pays $48.50 for 300 résumés. How much is the flat rate after the first 100 résumés are purchased?
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30. Alan earned a dollars last year. This year he received a raise of c dollars. He is paid biweekly. Express the difference algebraically between his total biweekly salary this year and last year.
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31. Adam works at an electronics store, earning $10.25 an hour, and is paid time and a half for any overtime. Last week, he worked 48 hours. His federal tax withheld is 15% and his state tax withheld is 4%. Social Security and Medicare taxes are also withheld. Determine his net pay for the week.
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32. An online job-search site charges employers fees to post job listings. The price for posting one job is $495.00. If four jobs are posted, the price per job is $450. What is the percent discount? (Round to the nearest tenth of a percent.)
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33. Leslye is a salesperson at a home improvement center. She is paid a monthly commission that is 7.5% of her first $1,000 in sales and 12% of the balance of her sales. Today she earned $517. What was the total value of the merchandise she sold?
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34. In Ramona’s state, the weekly unemployment compensation is 55% of the 26-week average for the two highest salaried quarters. Ramona made the same weekly salary for each of the 26 weeks in her two highest quarters. She will receive a weekly unemployment compensation check of $640. What were the total 26-week earnings for Ramona before she lost her job?
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35. David is a salesman for a local Ford dealership. He is paid a percent of the profit the dealership makes on each car. If the profit is under $800, the commission is 25%. If the profit is at least $800 and less than $1,000, the commission rate is 27.5% of the profit. If the profit is $1,000 or more, the rate is 30% of the profit. Find the difference between the commission paid if David sells a car for a $1,000 profit and the commission paid if he sells a car for a $799 profit?
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36. Kenya pays $66.32 biweekly for health insurance, which is 18% of the total cost. Her employer pays the rest. What is the employer’s annual contribution for Kenya’s health insurance?
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37. Isiah just accepted a job that pays an annual salary of $48,800 and was promised a 7.75% raise per year for the next five years if his performance goals are met. Isiah is confident he can meet these goals. What will his biweekly gross pay be when he begins his fifth year with the company?
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38. Elijah’s biweekly paycheck 5 years ago resulted in a direct deposit of $1,876.92 into his checking account each period. Today, he received a raise that brought his annual salary to $102.05K. If the benefits and taxes deducted from Elijah’s paycheck are approximately 36% of his gross pay, how much more per month will Elijah have in his monthly budget than he did 5 years ago? Round to the nearest dollar.
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39. Cherie accepted a job through an employment agency. The job pays $1,100 weekly. The agency charges 22% of her first three months, pay. How much money will the employment agency receive for placing Cherie in her new job? (Round to the nearest dollar.)
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Financial Algebra Solutions Manual Chapter 5 Page 87
© 2018 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or part.
Chapter 5
Lesson 5-1 Look for Employment
Check Your Understanding (Example 1)
K stands for $1,000.
$67.3K = $67.3 × $1,000 = $67,300
There are 12 months in a year.
$67,300 ÷ 12 = $5,608.33
Rounded to the nearest dollar, the monthly salary
is $5,608.
Check Your Understanding (Example 2)
The annual salary is x, so the monthly salary is .
12
x
The fee is 0.25 ,
12
x
× or 0.25 .
12
x
Check Your Understanding (Example 3)
The cost is $13 per line for 1–4 lines.
The cost is $13 × 4 = $68 for the first four lines and
$7.50 for each line over four.
To represent the number of lines over four, use the
expression x
− 4.
The piecewise function is
13 when 4
( ) .
68 7.5( 4) when 4
x x
c x x x
≤
= + − >
Extend Your Understanding (Example 3)
The cost is $k per line for 1, 2, 3, or 4 lines.
The cost is $k × 4 = $4k for the first 4 lines.
The piecewise function would be
when 4
( ) .
4 7.50( 4) when 4
kx x
c x k x x
≤
= + − >
Check Your Understanding (Example 4)
Since 31 > 20, there is a 16% discount, so the cost to
the employer is (100% – 16%) of the regular cost ,
which is 31x.
100 – 16 = 84
Take 84% of 31x:
0.84(31x) = 26.04x.
Check Your Understanding (Example 5)
Let n represent the number of batches of 100 cards
( ) ( )
2
2 2
p n n
c n p x n n n
≤
= + − >
when is an integer and
when is an integer and
Extend Your Understanding (Example 5)
200/p
Applications
1. In today’s world, you need to know how to find
job openings, and how to get your resume into
the hands of prospective employers once you
find them. With all of today’s technology, your
resume often exists in a sea of hundreds of
resumes, and making it stand out is crucial.
2. K stands for $1,000.
$47K = $47 × $1,000 = $47,000
There are 12 months in a year.
$47,000 ÷ 12 = $3,916.67
3. K stands for $1,000.
$64.5K = $64.5 × $1,000 = $64,500
There are 52 weeks in a year.
$64,500 ÷ 52 ≈ $1,240.38
Rounded to the nearest dollar, the weekly
salary is $1,240.38.
4. $52,400 ÷ 12 = $4,367
$4,367 × 0.25 = $1,091.67
5a. K stands for $1,000.
$51.2K = $51.2 × $1,000 = $51,200
There are 52 weeks in a year.
$51,200 ÷ 52 ≈ $984.6153846
Rounded to the nearest dollar, the weekly
salary is $984.62.
5b. $984.62 × 3 = $2,953.86
5c. $2,953.86 × 0.4 = $1,181.544
Rounded to the nearest dollar, the fee is
$1,182.
6a. From the table, if you post five jobs, each
posting is $320.
6b. 395
− 320 = $75
6c. 5(320) = $1,600
6d. 5(75) = $375
Financial Algebra Solutions Manual Chapter 5 Page 88
© 2018 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or part.
6e. Percent discount = Original price Discount price
Original price
−
1,975 1,600 19
1,975
− ≈ %
7a. $186.03
7b. Let x represent the number of batches of 100
resumes
( ) ( )
≤
= + − >
$91.50 2
$91.50 42 2 2
x x
c x x x x
when is an integer and
when is an integer and
8. There are 52 weeks in a year.
$575 × 52 = $29,900
K stands for $1,000.
$29,900 ÷ $1,000 = $29.9K
9. There are 12 months in a year.
$y × 12 = $12y
K stands for $1,000.
y
y K
12
$12 $1,000 $1,000
÷ =
10a. 2 < 3, so the cost of a two-line ad is $45.
3 = 3, so the cost of a three-line ad is $45.
$45
− $45 = $0
10b. $45 + $9(10
− 3) = $45 + $9(7) = $45 + $63 =
$108
10c. $45 + $9(11
− 3) = $45 + $9(8) = $45 + $72 =
$117
10d. Yes; the additional two lines will cost $18,
since each line over the first three lines costs
$9.
11a. 1 set = 100, which is not enough.
2 sets = 200, which is enough.
11b. $23 × 2 = $46
$46 × $0.08 = $3.68
$46 + $3.68 = $49.68
11c. 100% + 8% = 108% = 1.08
The function is r(x) = 1.08(23x).
12a. $34.6K = $34.6 × $1,000 = $34,600
$620 × 52 = $32,240
The job that pays $34,600, which is the stereo
job, pays more.
12b. $34,600 ÷ 52 ≈ $665.38
$665.38
− $620 = $45.38
Rounded to the nearest dollar, the difference
is $45.
13a. $585 ÷ 98 ≈ $5.97
13b. $675 ÷ 208 ≈ $3.25
13c. $675
− $585 = $90
208
− 98 = 110
The employer sees 110 extra resumes for $90.
$90 ÷ 110 ≈ $0.82
13d. An advantage is that the price per extra
resume is much less than the price of looking
at the original 100 resumes ($5.97 vs.
82 cents). The disadvantage is that the extra
resumes are from people far away, who would
most likely have to relocate to take the job.
Some may not be willing to, so time spent on
interviewing those people might be wasted
time.
Lesson 5-2 Pay Periods
and Hourly Rates
Check Your Understanding (Example 1)
Biweekly means checks every 2 weeks. There are
52 weeks in a year. 52 ÷ 2 = 26; each paycheck is
for x dollars, so the expression is 26x.
Check Your Understanding (Example 2)
Semi monthly means two checks every month.
There are 12 months in a year. 12 2 × 12 = 24
checks per year. The annual salary is divided into
24 checks, so the expression is 24
y .
Check Your Understanding (Example 3)
Roger’s pay per week is the hours he worked, h,
times his pay rate per hour, d. There are 52 weeks
in a year, so the expression is 52hd.
Check Your Understanding (Example 4)
Time-and-a-half means 1.5 times the pay rate,
so the expression is 1.5y.
Financial Algebra Solutions Manual Chapter 5 Page 89
© 2018 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or part.
Check Your Understanding (Example 5)
Ron’s regular pay is 40x. His overtime pay is
1.5 xy . His total weekly salary is 40x + 1.5xy.
Check Your Understanding (Example 6)
Regular pay Overtime pay Total pay
40 2(2 ) 484
40 4 484
44 484
11
x x
x x
x
x
+ =
+ =
+ =
=
=
Check Your Understanding (Example 7)
Jonathan’s regular pay is hr. His overtime pay is 2 ×
r × w, or 2rw. His total weekly salary is hr + 2rw.
Extend Your Understanding (Example 7)
Jovanna’s regular pay is 40r when she works 40
hours or less. Her overtime pay is 1.5 × r × (z
− 40)
when she works between 40 and 56 hours. Her
overtime pay is 2 × r × (z
− 56) when she works
more than 56 hours. When she works between 40
and 56 hours, she gets her regular pay plus her first
tier of overtime pay. When she works more than
56 hours, she gets her regular pay, her first tier of
overtime pay and her second tier of overtime pay.
The piecewise function is
40 when 40
( ) 40 1.5 ( 40) when 40 56.
40 1.5 (16) 2 ( 56) when 56
r z
p z r r z z
r r r z z
≤
= + − ≤ ≤
+ + − >
Check Your Understanding (Example 8)
The fifth year salary was $75,409. The eighth year
has three more increases of 4.1%.
75,409(1.041) 3 = 85,070 to the nearest dollar.
Applications
1. There are many talented people doing
excellent work who are underpaid, and there
are also many people being overpaid for
mediocre or poor work. Brando, being an
actor, may have been making a statement
about overpaid mediocre actors, but it extends
to the general workforce.
2. Semimonthly means two checks every month.
That is 24 checks in a year. Weekly means
52 checks every year.
52
− 24 = 28
3. Biweekly means every other week. That
means 52 ÷ 2 = 26 paychecks.
$42,500 ÷ 26 ≈ $1634.62
4. Semimonthly means twice a month. That is
24 paychecks.
24 × $1,371.50 = $32,916
5. $20,000,000 ÷ 65 ≈ $308,000 thousand, the
amount is $308,000.
6. Biweekly means every other week. That
means 52 ÷ 2 = 26 paychecks.
$1,763.28 × 26 = $45,845.28
7a. $478.25 × 52 = $24,869
7b. Semimonthly means twice a month. That is
24 paychecks.
$24,869 ÷ 24 ≈ $1,036.21
8a. Semimonthly means two checks every month.
That is 24 checks in a year. Biweekly means
every other week.
That is 52 ÷ 2 = 26 checks in a year.
26
− 24 = 2
8b. $72,000 ÷ 24 = $3,000
$72,000 ÷ 26 ≈ $2,769.23
$3,000
− $2,769.23 = $230.77
9a. Biweekly means every other week. That is
52 ÷ 2 = 26 checks in a year.
$38,350 ÷ 26 = $1,475
9b. Biweekly means every other week. That is
52 ÷ 2 = 26 checks in a year.
$46,462 ÷ 26 = $1,787
9c. $1,787
− $1,475 = $312
10. $76,000 + $12,500 = $88,500
$88,500 ÷ 12 = $7,375
11a. Semimonthly means two checks every month.
That is 24 checks in a year.
24 24
x
x ÷ =
11b. New salary = old salary + increase
New salary = x + y
( ) 24 24
x y
x y +
+ ÷ =
11c. 12 12 12
x y x y+ − =
Financial Algebra Solutions Manual Chapter 5 Page 90
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12. $15.50 × 29 = $449.50
13. $15.00 × x = $15x
14a. 40 × $16 = $640
14b. $16 × 1.5 = $24
14c. 43
− 40 = 3 overtime hours
3 × $24 = $72
14d. $640 + $72 = $712
15. 20 × $15.50 = $310
2 × $15.50 × 8 = $249
$310 + $249 = $558
16. 42
− 40 = 2 overtime hours
40 × $15.50 = $620
2 × 1.5 × $15.50 = $46.50
$620.00 + $46.50 = $666.50
17. 41
− 35 = 6 overtime hours
35 × $15.00 = $525.00 for the regular hours
6 × 1.5 × $15.00 = $135.00 for the overtime
hours
$525.00 + $135.00 = $659.00
$659.00
− $305.80 = $354.20
18. Colby: 1.5 × $18.00 = $27.00
Cheryl: 2 × $16.60 = $33.20
$33.20
− $27.00 = $6.20
Cheryl earns $6.20 more per hour for overtime.
19. There are 52 weeks in a year.
52 × 40 × x = 52(40x) or 2,080x
20. $21 × 40 = $840
$21 × 1.5 = $31.50
$840 ÷ $31.50 = 26.67
He needs to work 27 overtime hours in a week
for his overtime pay to be greater than his
regular pay.
21a. 40 1.5(8 ) $884
40 12 $884
52 $884
$17
x x
x x
x
x
+ =
+ =
=
=
21b. 1.5 × $17 = $25.50
22a. x × $13 = $13x
22b. 18% = 0.18
0.18 × y = 0.18y
22c. $13x + 0.18y
23a. 6 × $12 = $90
23b. 0.15 × $1,188 = $178.20
$178.20 × 0.25 = $44.55
23c. $90 + $44.55 = $134.55
23d. $134.55 ÷ 6 = $22.43
Rounded to the nearest dollar, the amount is
$22.43.
24. 52
− 3 = 49
Max works 49x hours.
52
− 4 = 48
Mindy works 48y hours.
The total is 49x + 48y.
25. $42,990 ÷ 52 ≈ $826.73
$1,277 ÷ 12 ≈ $106.42
$456 + $106.42 = $562.42
Yes; Gary’s weekly pay is $826.73, which
exceeds the $562.42 total cost of his monthly
car and insurance payments.
26a. Regular pay = regular hours × hourly rate =
B2*C2
26b. Overtime hours = hours worked
− regular
hours = A2
−B2
26c. Time-and-a-half rate = 1.5 × hourly rate =
1.5*C2
26d. Overtime pay = overtime hours × overtime rate
= E2*F2
26e. Total pay = regular pay + overtime pay =
D2 + G2
26f. The completed spreadsheet (missing entries)
is shown below.
D E F G H
2 $640 2 $24 $48 $688
3 $760 4 $28.50 $114 $874
4 $632 5 $23.70 $118.50 $750.50
Financial Algebra Solutions Manual Chapter 5 Page 91
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27a–c. The grid is shown below.
1
0.01
2
0.02
3
0.04
4
0.08
5
0.16
6
0.32
7
0.64
8
1.28
9
2.56
10
5.12
11
10.24
12
20.48
13
40.96
14
81.92
15
163.84
16
327.68
17
655.36
18
1,310.72
19
2,621.44
20
5,242.88
21
10,485.76
22
20,971.52
23
41,943.04
24
83,886.08
25
167,772.16
26
335,544.32
27
671,088.64
28
1,342,177.28
29
2,684,354.56
30
5,368,709.12
31
10,737,418.24
27d. The pay exceeds $1,000,000 for the first time
on the 28th .
27e. The minimum on the x-axis is 0, the maximum
is 30, and the scale is 1. The minimum on the
y-axis is 0, the maximum is 90, and the scale
is 10. Enter the day number in L1 and the
salary in L2. Use the STAT PLOT feature
on your graphing calculator to graph the
scatterplot. The display should look similar
to the one below.
27f. Since the exponent is 13, there were 13 days
of doubling, so including the first day, this is
the 14th day’s salary.
28. $2 × 52 × 20 = $2,080
The purchase of a $2 ticket each week for
20 years cost $2,080 and her winnings were
$2,000. This was not a worthwhile investment.
Lesson 5-3 Commissions,
Royalties, and Piecework Pay
Check Your Understanding (Example 1)
Total book sales = xy. Xander’s commission from
total book sales = 0.08xy. Total income = 0.08xy +
2,500
Check Your Understanding (Example 2)
There are two cases. When y ≤ x, he only gets 7%
on his sales, or 0.07x. When y > x, he gets 7% on x
and 10% on the difference between y and x.
The piecewise function is
0.07 0.10( ) when
( ) .
0.07 when
x y x y x
f x x x y
+ − >
= ≥
Check Your Understanding (Example 3)
Total income = p × s = ps
Check Your Understanding (Example 4)
Divide her total earnings x by 0.11 to find the
number of crates she picked.
0.11
x
Check Your Understanding (Example 5)
0.22 × $750 = $165
0.20 × $749 = $149.80
$165
− $149.80 = $15.20
Check Your Understanding (Example 6)
Commission for the first $1,000 = 0.06 × $1,000
Balance of sales after $1,000 = x
− $1,000
Commission for the balance = 0.11(x
− 1,000)
0.06(1,000) + 0.11(x
− 1,000) = 203
60 + 0.11x
− 110 = 203
0.11x
− 50 = 203
0.11x = 253
x = 2,300
The total sales were $2,300.
Financial Algebra Solutions Manual Chapter 5 Page 92
© 2018 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or part.
Applications
1. To many people, money is a top priority. Many
people feel that money buys happiness, and,
as a result, they go to great lengths to acquire
it.
2a. $991,000(1.09) = 1,080,190
2b. $550,000(9) = 4,950,000
2c. $1,080,190 + 4,950,000 = 6,030,190
2d. $6,030,190(0.15) = $904,528.50
3. $8,870 × 0.25 = $2,217.50
4. $200 + (0.03 × $29,700)
= $200 + $891 = $1,091
5. $1,000 × 0.12 = $120
$7,500
− $1,000 = $6,500
$6,500 × 0.15 = $975
$120 + $975 = $1,095
6. $1,715,000 + (0.10 × 300,000 × $24)
= $1,715,000 + $720,000
= $2,435,000
7. $250,000 + $310,000 = $560,000
$560,000 × 0.065 = $36,400
8. Hourly: 35 × $12.60 = $441
Commission: $230 × 0.05 = $11.50
$441 + $11.50 = $452.50
9. Hourly: 20 × $16 = $320
Commission: $2,100 × 0.08 = $168
$320 + $168 = $488
10. 731 × $0.58 = $423.98
11a. $1,000 × x = $10
$10 1.00 1%
$1,000 = =
11b. $y × x = $x
x
y is the decimal.
(100)
x
y is the percent.
12. 100 × $0.92 = $92
120
− 100 = 20
20 × $1.01 = $20.20
$92 + $20.20 = $112.20
13a. 2,000 × $0.25 = $500
13b. $500
− $474 = $26
14a. 755 × $0.12 = $90.60
14b. 38 × $12 = $456
14c. $90.60 + $456 = $546.60
14d. Producing 0 units would result in hourly pay
only, which is 38 × $12 = $456.
15. 80 × $0.50 = $40
50 × $0.90 = $45
Bushels over 100 = x
− 100
$85 + $0.95(x
− 100)
16. 30 × $156 = $4,680
17. $252.48
$0.12 $252.48 2,104
$0.12
x × = = =
18a. 375 + 22 + 410 + 390 + 390 = 1,587
1,587 317.4
5 =
18b. In order: 22, 275, 390, 390, 410.
The median is the number in the middle, which
is 390.
18c. The mode is the most common number, which
is 390.
19a. $6,300 × 0.07 = $441
19b. $441 ÷ 5 = $88.20
20. 0.14x = $1,233.60
x ≈ $8,811.43
To the nearest dollar, the amount is $8,811.
21. 0.095 × $1,000 = $95
Balance of sales after $1,000 $1,000
95 0.155( 1,000) 1,234.25
95 0.155 155 1,234.25
0.155 60 1,234.25
0.155 1,294.25
8,350
x
x
x
x
x
x
= −
+ − =
+ − =
− =
=
=
The total sales were $8,350.
22a. $1,500 is in the third part of the piecewise
function, so the commission rate is 0.25, or
25%.
22b. $900 is in the second part of the piecewise
function, so the commission rate is 0.23, or
23%.
22c. $970 × 0.23 = $223.10
Financial Algebra Solutions Manual Chapter 5 Page 93
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22d. $33,200
− $32,090 = $1,110
$1,110 × 0.23 = $255.30
23a. There are three cases. The piecewise function
is
0.17 when0 500
( ) 0.20 when500 1,100.
0.22 when 1,100
x x
c x x x
x x
≤ ≤
= < ≤
>
23b. $22,800
− $21,696 = $1,104
$1,104 × 0.22 = $242.88
23c. $1,104 × 0.25 = $276
$276
− $242.88 = $33.12
24. profit: c
− d
Commission: 0.24(c
− d)
25. 0.10 × $2,000 = $200
x
x
x
x
x
x
Balance of sales after $2,000 $2,000
200 0.12( 2,000) 231.20
200 0.12 240 231.20
0.12 40 231.20
0.12 271.20
2,260
= −
+ − =
+ − =
− =
=
=
The total sales were $2,260.
Lesson 5-4 Employee Benefits
Check Your Understanding (Example 1)
The number of paid vacation days goes up by 2 for
each year worked. The number of days starts at 5.
The equation is y = 2x + 5.
Check Your Understanding (Example 2)
Biweekly means every other week. Mark gets 52 ÷ 2
= 26 paychecks. He pays d dollars each time, for a
total of 26d. Divide by p to get the total cost of
Mark’s coverage in terms of d and p. The total cost
is 26 .
p
d
Check Your Understanding (Example 3)
The average of the last three year’s salaries is
.
3
A B C+ + The expression is 0.02 .
3
A B C
D + +
Check Your Understanding (Example 4)
0.60 × x = $360
x = $600
$600 × 26 = $15,600
Extend Your Understanding (Example 4)
0.60 × x = $570
x = $950
Her weekly salary was $950.
Applications
1. Perhaps one of the biggest employee benefits
a person can attain from work is the joy of that
work. Pearl Buck implies that if you find that
joy, then you have discovered a treasure.
2a. The number of paid vacation days goes up by
2 for each 6-months worked. The number of
days starts at 3. The equation is y = 2x + 3, or
y = 3 + 2x.
2b. 4.4 years = eight 6-month periods.
Substitute 8 for x in y = 2x + 3.
2(8) + 3 = 16 + 3 = 19
He will have earned 19 days.
3a. The number of paid vacation days goes up by
3 for each year worked. The number of days
starts at 2. The equation is y = 3x + 2, or y =
2 + 3x.
3b. Substitute 5 for x in y = 3x + 2.
3(5) + 2 = 15 + 2 = 17
She will have earned 17 days.
3c. a1 = 2, d = 3
3d. 4 weeks = 4 × 5 = 20 days
20 = 3x + 2
18 = 3x
6 = x
She will have reached the maximum after
6 years.
4a. The number of paid vacation days goes up by
2 for each year worked. The relationship is
y = 2x.
4b. 18 = 2x
9 = x
It will take 9 years to earn 18 paid vacation
days.
5a. The number of paid vacation days doubles for
each year worked. The relationship is
exponential and is y = 2x.
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5b. Substitute 4 for x in y = 2x.
24 = 16
She will have earned 16 days.
5c. 5 weeks = 5 × 5 = 25 days
25 = 2x
25 = 32, so he will have reached the maximum
after 5 years.
6. $67.50 × 26 = $1,755
$1,755 ÷ 0.18 = $9,750
7a. $47,700 < $55,000, so Arielle pays $60 per
month.
$60 × 12 = $720
$720 ÷ 0.05 = $14,400
$14,400
− $720 = $13,680
7b. $68,300 > $55,000, so family coverage is
$115 per month. $115 + $935 = $1,050
$115 ÷ $1,050 = 0.15 = 15%
8. The average of the last four year’s salaries is
$82,000 $96,000 $105,000 $109,000
4
$392,000 $98,000.
4
+ + +
= =
1.2% × 20 × $98,000 = 0.012 × 20 × $98,000
= $23,520
9. The average of the three highest salaries is
$97,000 $97,800 $98,198
3
$292,998 $97,666.
3
+ +
= =
1.65% × 27 × $97,666 = 0.0165 × 27 × $97,666
= $43,510.203
Rounded to the nearest cent, the amount is
$43,510.20.
10a. The salaries are in cells B3, B4, B5, B6. The
formula is average(B3:B6). Other formulas are
sum(B3:B6)/4 or = (B3+B4+B5+B6)/4.
10b. Divide the pension percentage by 100. Then
multiply by the average salary and the number
of years worked. The formula is
B1/100*B7*B2.
11. $715 + $700 + $730 + $730 + $730 + $720 +
$700 + $720 + $720 + $720 + $725 + $720 +
$725 + $730 + $730 + $735 + $735 + $735 +
$740 + $740 + $740 + $740 + $740 + $740 +
$740 + $740 = $715 + 2($700) + 5($730) +
5($720) + 2($725) + 3($735) + 8($740) =
$18,940
$18,940 ÷ 26 ≈ $728.46
$728.46 × 0.55 = $400.653
To the nearest cent, the amount is $400.65.
12. $13,950.80 + $14,250.10 = $28,200.90
$28,200.90 ÷ 26 = $1,084.65
$1,084.65 × 0.65 = $705.0225
To the nearest cent, the amount is $705.02.
Lesson 5-5 Social Security
and Medicare
Check Your Understanding (Example 1)
Medicare tax is 1.45% of all income, so Lisa paid
–.0145x.
Check Your Understanding (Example 2)
Her combined income was x + y + z, which was less
than the maximum taxable amount.
Social Security is 6.2% or 0.062(x + y + z).
Medicare is 1.45%, or 0.145(x + y + z).
0.062(x + y + z) + 0.145(x + y + z)
= 0.0765(x + y + z)
Check Your Understanding (Example 3)
When the Social Security tax is $3,500, the line is
between $40,000 and $60,000 on the horizontal
axis, closer to $60,000. The taxable income is about
$55,000.
Check Your Understanding (Example 4)
From Example 4, the tax rate in 1988 was 7.51%.
0.0751x = $2,853.80
$2,853.80 $38,000
0.0751
x = =
Financial Algebra Solutions Manual Chapter 5 Page 95
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Applications
1. A nation is stronger when its people are cared
for. The Social Security program does just that.
2a. $17,700 × 0.0605 = $1,070.85
2b. $25,900 × 0.0613 = $1,587.67
2c. $32,400 × 0.067 = $2,170.80
2d. $37,800 × 0.067 = $2,532.60
2e. $42,000 × 0.0715 = $3,003.00
2f. $45,000 × 0.0751 = $3,379.50
2g. $51,300 × 0.0765 = $3,924.45
3a. $78,000 ÷ 12 = $6,500
3b. The maximum amount in 1990 was $51,300.
$51,300 ÷ $6,500 ≈ 7.89
August is the 8th month, so he would reach the
maximum in August.
3c. $6,500 × 0.0765 = $497.25
3d. December is past August, so the amount is $0.
4a. $48,000 ÷ 12 = $4,000
4b. The maximum amount in 1978 was $17,700.
$17,700 ÷ $4,000 = 4.425
May is the 5th month, so she reached the
maximum in May.
4c. $4,000 × 0.605 = $242
4d. Dawn earned $4,000 per month. Form January
– April, she earned $16,000. Since the Social
Security maximum taxable income for 1978
was $17,700, Danw had to pay 6.05% of 1,700
in May.
0.0605(1,700) = $102.85
4e. November is past May, so the amount is $0.
5a. Social Security: $57,600 × 0.062 = $3,571.20
Medicare: $135,000 × 0.0145 = $1,957.50
3,571.20 + 1,957.50 = 5,528.70.
5b. The maximum is $84,900 × 0.062 = $5,263.80.
The piecewise function is
0.062 when0 84,900
( ) .
5,263.80 when 84,900
x x
f x x
< ≤
= >
6. The maximum is $57,600 × 0.062 = $3,571.20.
The piecewise function is
0.062 when0 57,600
( ) 3,571.20 when 57,600
x x
f x x
< ≤
= >
The graph is shown below.
The cusp is at (57600, 3571.20).
7. Social Security:
The maximum is $55,500 × 0.062 = $3,441.00.
The piecewise function is
0.062 when0 55,500
( ) .
3,441.00 when 55,500
x x
f x x
< ≤
= >
The cusp is at (55,500, 3,441.00).
Medicare: The maximum is $125,000 ×
0.0145 = $1,812.50.
The piecewise function is
0.0145 when0 125,000
( ) .
1,812.50 when 125,000
x x
f x x
< ≤
= >
The cusp is at (125,000, 1,812.50).
The graph is shown below.
8. $2,136
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9. Assuming her income was proportional per
month, her income in February was .
12
p
The Social Security tax is 0.062 .
12
p
10. Social Security is 6.2% or 0.062d.
Medicare is 1.45%, or 0.145d.
0.062d + 0.145d = 0.0765d
11a. $5,600 × 12 = $67,200
$67,200 < $94,200
She earned less than the maximum taxable
income.
11b. Annual income is 12×.
Social Security is 6.2% or 0.062(12×).
0.062(12×) = 0.744×
11c. Annual income is 12×.
Medicare is 1.45% or 0.0145(12×).
0.0145(12×) = 0.174×
12. A slope of 1 means the Social Security
contribution would be 100% of the income.
13. They will pay a very high Social Security tax
and may pay more than they are able to get
from the Social Security system.
14. See students’ work. These answers will vary
from year to year.
15. The Social Security tax jumps at $100,000.
If you make $99,999.99, you would pay very
close to $6,000. But, if your income is just
2 cents more, $100,000.01, you would pay
$2,000 more in taxes.
16. $99,112 + $56,222 = $155,334
$155,334
− $118,500 = $36,834
$36,834 × 0.062 = $2,283.71
To the nearest cent, the amount is $2,283.71.
17. Answers vary depending on the current year.
Divide the annual salary by the 162 games.
$25,000,000/162 ≈ $154,320.99
For example, in 2017, the maximum taxable
amount was $127,200. The player earns more
than the maximum taxable amount in the first
game of the year.
Assessment
Really? Really! Revisited
The sorting was done by determining the percent
change in employment numbers from 2014 to 2024.
For example, wind turbine service technicians
increased by 4,800 from 2014 to 2024. This
represents a 109% increase over the 10-year
period. By calculating the percent increase over the
10-year period for each occupation, you will see
how the jobs have been ranked.
Applications
1. K stands for $1,000.
$44.5K = $44.5 × $1,000 = $44,500
There are 52 weeks in a year.
$44,500 ÷ 52 ≈ $855.77
2. $51K = $51 × $1,000 = $51,000
$51,000 ÷ 12 = $4,250
$4,250 × 0.35 = $1,487.50
3. Six-line ad: $32 + $9(6
− 3) = $32 + $9(3)
= $32 + $27 = $59
Seven-line ad: $32 + $9(7
− 3) = $32 + $9(4)
= $32 + $36 = $68
$68
− $59 = $9
4. + =
+ =
=
=
40 1.5(5 ) $926.25
40 7.5 $926.25
47.5 $926.25
$19.50
x x
x x
x
x
5. 43
− 40 = 3 overtime hours
40 × $16.00 = $640.00
3 × 1.5 × $16.00 = $72
$640.00 + $72 = $712
6. There are 52 weeks in a year.
52(40x + 3 × 1.5x) = 52(40x + 4.5x) = 52(44.5x)
= 2,314x
7. Total manual sales = xy.
Author’s commission from total book sales =
0.10xy.
Total income = 0.10xy + 1,000
Financial Algebra Solutions Manual Chapter 5 Page 97
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8. 0.71 × x = $291.81
$298.81 411
0.71
x = =
9. $60
10. There are three cases. The piecewise function
is
0.18 when 900
( ) 0.20 when900 1500.
0.25 when 1,500
x x
c x x x
x x
≤
= < ≤
>
11. $1,000 × 0.04 = $40
Amount over 1,000 = x
− 1,000
$40 + 0.06(x
− 1,000)
12. $28.80 × 52 = $1,497.60
$1,497.60 ÷ 0.15 = $9,984
13. The average of the last five salaries is
$92,000 $92,800 $99,000 $100,500 $105,000
5
$489,300 $97,860.
5
+ + + +
= =
1.45% × 22 × $97,860 = 0.0145 × 22 × $97,860
= $31,217.34
14. $19,574 + $21,974 = $41,548
$41,548 ÷ 26 = $1,598
$1,598 × 0.47 = $751.06
15a. The maximum Social Security is $102,000 ×
0.062 = $6,324.
The piecewise function is
0.062 0.0145 when 102,000
( ) .
6,324 0.0145 when 102,000
x x x
f x x x
+ <
= + ≥
15b. $143,000 > $102,000
$102,000 × 0,062 = $6,324
15c. $143,000 × 0.0145 = $2,073.50
16a. 1980: FICA and Medicare combined is
$1,587.67 1990: FICA and Medicare combined
is $3,924.45 2000: FICA is $4,724.40 and
Medicare depends on salary. 2010: FICA is
$6,621.60 and Medicare depends on salary.
16b. $7,933.93
17. Divide the amount in cell B1 by 100.
Assuming 0’s are entered in for the quarters
that are not the two highest, the formula is
=(sum(B3:B6)/26)*B1/100.
Original price was: $30.00.$20.00Current price is: $20.00.
Original price was: $30.00.$20.00Current price is: $20.00.
Original price was: $30.00.$20.00Current price is: $20.00.
Original price was: $30.00.$20.00Current price is: $20.00.
Original price was: $30.00.$20.00Current price is: $20.00.
Original price was: $30.00.$20.00Current price is: $20.00.
