Chapter 6
Lesson 6-1 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.
Check Your Understanding (Example 2)
Check Your Understanding (Example 3)
Extend Your Understanding (Example 3)
Check Your Understanding (Example 4)
Check Your Understanding (Example 5)
Jane’s price = 0.39(77) = $30.03. From the
information in Example 5, Pete would need to order
1 set of copies. From the piecewise function in
Example 5, the cost would be $29.95. Pete can get
100 copies (or even 200 copies) for $29.95, which
is less expensive than paying per copy.
Extend Your Understanding (Example 5)
The unit price paying per copy is $0.39. The unit
Applications
find them. With all of today’s technology, your
resume often exists in a sea of hundreds of
$34,500 ÷ 52 ≈ $663.4615385
Rounded to the nearest dollar, the weekly salary
6a. K stands for $1,000.
$51.2K = $51.2 × $1,000 = $51,200
7a. From the table next to Example 4, 5–20 postings
7d. $75 × 5 = $375
Rounded to the nearest percent, the savings is
19%.
8a. The first 200 copies cost $21.50. The next 200
8b. The cost is $21.50 per set for 1 or 2 sets. The
cost is $21.50 for the first 2 sets and $x for each
9. There are 52 weeks in a year.
K stands for $1,000.
$29,900 ÷ $1,000 = $29.9K
10. There are 12 months in a year.
$y × 12 = $12y
11a. 2 < 3, so the cost of a 2-line ad is $45.
11b. $45 + $9(10 – 3) = $45 + $9(7) = $45 + $63
11c. $45 + $9(11 – 3) = $45 + $9(8) = $45 + $72
11d. Yes; the additional two lines will cost $18, since
12a. 1 set = 100, which is not enough.
12b. $23 × 2 = $46
12c. 100% + 8% = 108% = 1.08
13a. $34.6K = $34.6 × $1,000 = $34,600
13b. $34,600 ÷ 52 ≈ $665.38
14a. $585 ÷ 98 ≈ $5.97
14b. $675 ÷ 208 ≈ $3.25
$90 ÷ 110 ≈ $0.82
14d. An advantage is that the price per extra resume
to, so time spent on interviewing those people
Lesson 6-2 Pay Periods
and Hourly Rates
Check Your Understanding (Example 1)
are 12 months in a year. 12 × 2 = 24; the annual
y
12
Roger’s pay per week is the hours he worked, h,
Check Your Understanding (Example 4)
Check Your Understanding (Example 5)
1.5xy.
Check Your Understanding (Example 6)
40x + 2(2x) = 484
Check Your Understanding (Example 6)
Extend Your Understanding (Example 6)
Jovanna’s regular pay is 40r when she works 40
hours or less. Her overtime pay is 1.5 × r × (z – 40)
z40 when 40
r
≤
⎧
⎪
Applications
1. There are many talented people doing excellent
work who are underpaid, and there are also
2. Semimonthly means 2 checks every month.
52 – 24 = 28
4. Semimonthly means twice a month. That is 24
paychecks.
5. $27,708,525 ÷ 158 ≈ $175,371
6. Biweekly means every other week. That means
$1,763.28 × 26 = $45,845.28
paychecks.
$24,869 ÷ 24 ≈ $1,036.21
8a. Semimonthly means 2 checks every month.
8b. $72,000 ÷ 24 = $3,000
9a. Biweekly means every other week. That is 52 ÷
9b. Biweekly means every other week. That is 52 ÷
9c. $1,787 – $1,475 = $312
10. $76,000 + $12,500 = $88,500
$88,500 ÷ 12 = $7,375
11a. Semimonthly means 2 checks every month.
x
11b. New salary = Old salary + increase
x
11c. +
x
y
24 –
x
24 = y
24
16. 42 – 40 = 2 overtime hours
17. 41 – 35 = 6 overtime hours
35 × $9.20 = $322.00
$404.80 – $305.80 = $99
18. Colby: 1.5 × $8.90 = $13.35
$14.20 – $13.35 = $0.85
19. There are 52 weeks in a year.
20. $10 × 40 = $400
21a. 40x + 1.5(8x) = $1,248
21b. 1.5 × $24 = $36
22c. $5.90x + 0.18y
23a. 6 × $11 = $66
25. $42,990 ÷ 52 ≈ $826.73
exceeds the $562.42 total cost of his monthly
car and insurance payments.
26b. overtime hours = hours worked – regular hours
=A2–B2
26c. time-and-a-half rate = 1.5 × hourly rate
26d. overtime pay = overtime hours × overtime rate
26e. total pay = regular pay + overtime pay
27a-c. The grid is shown below.
1
0.01
2
0.02
3
0.04
4
0.08
2.56
5.12
10.24
20.48
167,772.16
335,544.32
671,088.64
1,342,177.28
29
30
31
27d. The pay exceeds $1,000,000 for the first time on
27e. The minimum on the x-axis is 0, the maximum is
10. Enter the day number in L1 and the salary in
Lesson 6-3 Commissions,
Royalties, and Piecework Pay
Check Your Understanding (Example 1)
Check Your Understanding (Example 2)
Check Your Understanding (Example 3)
Check Your Understanding (Example 4)
x = 0.11 × number of crates
Check Your Understanding (Example 3)
Check Your Understanding (Example 6)
Commission for the first $1,000 = 0.06 × $1,000
0.11x – 50 = 203
Applications
1. To many people, money is a top priority. Many
2a. 1,000,000 × $5 = $5,000,000
2b. 550,000 × $6 = $3,300,000
2c. $5,000,000 + $3,300,000 = $8,300,000
2d. $8,300,000 × 0.15 = $1,245,000
5. $1,000 × 0.12 = $120
6. $1,715,000 + (0.10 × 300,000 × $24)
7. $250,000 + $310,000 = $560,000
8. Hourly: 35 × $9.60 = $336
$200 + $168 = $368
10. 731 × $0.28 = $204.68
11a. $1,000 × x = $50
11b. $y × x = $x
12. 100 × $0.92 = $92
120 – 100 = 20
20 × $1.01 = $20.20
$92 + $20.20 = $112.20
13a. 2,000 × $0.25 = $500
14a. 755 × $0.12 = $90.60
14c. $90.60 + $304 = $394.60
14d. Producing 0 units would result in hourly pay
50 × $0.90 = $45
Bushels over 100 = x – 100
$85 + $0.95(x – 100)
16. 30 × $156 = $4,680
19. x × $0.12 = $252.48 = $.252 48
$0.12 = 2,104
5 = 317.4
20b. In order: 22, 275, 390, 390, 410.
is 390.
22. 0.14x = $1,233.60
23. 0.095 × $1,000 = $95
Balance of sales after $1,000 = $1,000 – x
95 + 0.155(x – 1,000) = 1,234.25
0.155x = 1,294.25
25%.
24b. $900 is in the second part of the piecewise
function, so the commission rate is 0.23, or
23%.
24c. $970 × 0.23 = $223.10
24d. $33,200 – $32,090 = $1,110
25a. There are 3 cases. The piecewise function is
25b. $22,800 – $21,696 = $1,104
$1,104 × 0.22 = $242.88
26. profit: c – d
Commission: 0.24(c – d)
27. 0.10 × $2,000 = $200
Lesson 6-4 Employee Benefits
Check Your Understanding (Example 1)
The number of paid vacation days goes up by 2 for
Check Your Understanding (Example 2)
Biweekly means every other week. Mark gets 52 ÷
2 = 26 paychecks. He pays d dollars each time, for
Check Your Understanding (Example 3)
Check Your Understanding (Example 4)
$600 × 26 = $15,600
Extend Your Understanding (Example 4)
0.60 × x = $570
Applications
1. Perhaps one of the biggest employee benefits a
person can attain from work is the joy of that
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
3b. Substitute 5 for x in y = 3x + 2.
3(5) + 2 = 15 + 2 = 17
She will have earned 17 days.
3c. 4 weeks = 4 × 5 = 20 days
6 years.
It will take 9 years to earn 18 paid vacation days.
5a. The number of paid vacation days doubles for
5b. Substitute 4 for x in y = 2x.
5c. 5 weeks = 5 × 5 = 25 days
6. $67.50 × 26 = $1,755
7a. $47,700 < $55,000, so Arielle pays $40 per
7b. $68,300 > $55,000, so family coverage is $165
8. The average of the last four year’s salaries is
4 = $98,000.
1.2% × 20 × $98,000 = 0.012 × 20 × $98,000
= $23,520
9. The average of the three highest salaries is
3 =
$,292 998
3 = $97,666.
10a. The salaries are in cells B3, B4, B5, B6. The
=sum(B3:B6)/4 or =(B3+B4+B5+B6)/4.
10b. Divide the pension percentage by 100. Then
11. $715 + $700 + $730 + $730 + $730 + $720 +
Lesson 6-5 Social Security and
Medicare
Check Your Understanding (Example 1)
Check Your Understanding (Example 2)
less than the maximum taxable amount.
Social Security is 6.2% or 0.062(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
Check Your Understanding (Example 4)
From Example 4, the tax rate in 1988 was 7.51%.
Applications
1. A nation is stronger when its people are cared
2a. $17,700 × 0.0605 = $1,070.85
2d. $37,800 × 0.067 = $2,532.60
4a. $48,000 ÷ 12 = $4,000
4b. The maximum amount in 1978 was $17,700.
4c. $4,000 × 0.605 = $242
4d. November is past May, so the amount is $0.
5a. Social Security: $57,600 × 0.62 = $3,571.20
Medicare: $135,000 × 0.145 = $1,957.50
5b. The maximum is $84,900 × 0.062 = $5,263.80.
The piecewise function is
6. The maximum is $57,600 × 0.062 = $3,571.20.
The piecewise function is
The graph is shown below.
7. Social Security:
The maximum is $55,500 × 0.062 = $3,441.00.
The cusp is at (55,500, 3,441.00).
Medicare: The maximum is
$125,000 × 0.0145 = $1,812.50.
The piecewise function is
.
The graph is shown below.
.,
() ,. ,
<≤
⎧
=⎨>
xx
fx x
0 0145 when 0 125 000
8. Assuming her income was proportional per
10a. $5,600 × 12 = $67,200
10b. Annual income is 12x.
Social Security is 6.2% or 0.062(12x).
10c. Annual income is 12x.
Medicare is 1.45% or 0.0145(12x).
11. A slope of 1 means the Social Security
12. They will pay a very high Social Security tax and
13. See students’ work. These answers will vary
14. The Social Security tax jumps at $100,000. If
15. $99,112 + $56,222 = $155,334
16. $25,000,000 ÷ 162 ≈ $154,320.99
Assessment
Really? Really! Revisited
change in employment numbers from 2006 to
53.4% increase over the ten-year period. By
Applications
$44,500 ÷ 52 ≈ $855.77
2. $51K = $51 × $1,000 = $51,000
$4,250 × 0.35 = $1,487.50
3. 6-line ad: $32 + $9(6 – 3) = $32 + $9(3)
7-line ad: $32 + $9(7 – 3) = $32 + $9(4)
$68 – $59 = $9
47.5x = $451.25
5. 43 – 40 = 3 overtime hours
52(40x + 3 × 1.5x) = 52(40x + 4.5x) = 52(44.5x)
= 0.10xy.
9. There are 3 cases. The piecewise function is
.
.
() . ,
≤
⎧
⎪
=<
⎨
xx
cx x x
0 18 when 900
0 20 when 900 1500
≤
10. $1,000 × 0.04 = $40
11. $28.80 × 52 = $1,497.60
15a. $80,400 > $76,200
2000 Social Security: $76,200 × 0.062
= $4,984.80
= $6,150.60
12. The average of the last five salaries is
$, $, $, $ , $ ,+++ +92 000 92 800 99 000 100 500 105 000
13. $19,574 + $21,974 = $41,548
14a. The maximum Social Security is $102,000 ×
14b. $143,000 > $102,000
when the salary was less than the maximum.
The more you make, the smaller percentage of
your salary is used.
16. Divide the amount in cell B1 by 100.