Algebra Foundations for Normal People by Gabriel Beguerie - HTML preview
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Chapter 4
Worked example (no skipped steps)
4.1 Convert 0 . 08 to a percent.
Move the decimal point two places to the right:
0 . 08 = 8%
Answer: 8%.
Worked example (no skipped steps)
4.2 Convert 62% to a decimal.
Move the decimal point two places to the left:
62% = 0 . 62
Answer: 0 . 62.
Worked example (no skipped steps)
4.3 Convert 3 to a decimal and a percent.
5
Divide numerator by denominator:
3 = 0 . 6
5
Now convert to a percent:
0 . 6 = 60%
Answer: 3 = 0 . 6 = 60%.
5
Step-by-step solutions
Worked example (no skipped steps)
4.4 Convert 125% to a decimal.
Move the decimal point two places to the left:
125% = 1 . 25
Answer: 1 . 25.
Worked example (no skipped steps)
4.5 Convert 0 . 375 to a fraction and a percent.
As a fraction:
375
0 . 375 = 1000
Simplify by dividing top and bottom by 125:
375
3
=
1000
8
As a percent:
0 . 375 = 37 . 5%
Answer: 3 and 37 . 5%.
8
Worked example (no skipped steps)
4.6 Find 15% of 80.
Convert the percent:
15% = 0 . 15
Multiply:
0 . 15 · 80 = 12
Answer: 12.
Worked example (no skipped steps)
4.7 Find 8% of 250.
Convert:
8% = 0 . 08
Multiply:
0 . 08 · 250 = 20
Answer: 20.
147
Worked example (no skipped steps)
4.8 Find 25% of 96.
Since 25% = 1 ,
4
1 · 96 = 24
4
Answer: 24.
Worked example (no skipped steps)
4.9 Find 150% of 40.
Convert:
150% = 1 . 5
Multiply:
1 . 5 · 40 = 60
Answer: 60.
Worked example (no skipped steps)
4.10 Find 12 . 5% of 64.
Convert:
1
12 . 5% = 0 . 125 = 8
Now multiply:
1 · 64 = 8
8
Answer: 8.
Worked example (no skipped steps)
4.11 A $40 shirt is discounted by 30%. Find the sale price.
A 30% discount leaves 70% of the price:
70% = 0 . 70
Multiply:
0 . 70 · 40 = 28
Answer: the sale price is $28.
Step-by-step solutions
Worked example (no skipped steps)
4.12 A $120 item has 8% sales tax. Find the total cost.
Sales tax means multiply by:
1 + 0 . 08 = 1 . 08
Now compute:
1 . 08 · 120 = 129 . 6
Answer: the total cost is $129.60.
Worked example (no skipped steps)
4.13 A value of 50 increases by 10%. Find the new value.
Multiply by:
1 + 0 . 10 = 1 . 10
Then:
1 . 10 · 50 = 55
Answer: the new value is 55.
Worked example (no skipped steps)
4.14 A value of 200 decreases by 8%. Find the new value.
Multiply by:
1 − 0 . 08 = 0 . 92
Then:
0 . 92 · 200 = 184
Answer: the new value is 184.
Worked example (no skipped steps)
4.15 A test score rises from 60 to 72. Find the percent increase.
Find the change:
72 − 60 = 12
Divide by the original value:
12 = 0 . 2
60
Convert to a percent:
0 . 2 = 20%
Answer: 20% increase.
149
Worked example (no skipped steps)
4.16 A price rises from $50 to $65. Find the percent increase.
Change:
65 − 50 = 15
Divide by the original:
15 = 0 . 3
50
Convert:
0 . 3 = 30%
Answer: 30% increase.
Worked example (no skipped steps)
4.17 A score drops from 90 to 72. Find the percent decrease.
Change:
90 − 72 = 18
Divide by the original:
18 = 0 . 2
90
Convert:
0 . 2 = 20%
Answer: 20% decrease.
Worked example (no skipped steps)
4.18 A population falls from 800 to 680. Find the percent decrease.
Change:
800 − 680 = 120
Divide by the original:
120 = 0 . 15
800
Convert:
0 . 15 = 15%
Answer: 15% decrease.
Step-by-step solutions
Worked example (no skipped steps)
4.19 A recipe uses 20% of a 500-gram bag of sugar. How many grams is that?
Convert:
20% = 0 . 20
Multiply:
0 . 20 · 500 = 100
Answer: 100 grams.
Worked example (no skipped steps)
4.20 A bank balance of $400 grows by 5%. What is the new balance?
Multiply by:
1 + 0 . 05 = 1 . 05
Then:
1 . 05 · 400 = 420
Answer: the new balance is $420.
Worked example (no skipped steps)
4.21 A phone plan costs $50 and gets a 12% discount. What is the discounted price?
A 12% discount leaves:
100% − 12% = 88% = 0 . 88
Multiply:
0 . 88 · 50 = 44
Answer: the discounted price is $44.
Worked example (no skipped steps)
4.22 Convert 7 to a decimal and a percent.
8
Divide:
7 = 0 . 875
8
Convert to a percent:
0 . 875 = 87 . 5%
Answer: 0 . 875 and 87 . 5%.
151
Worked example (no skipped steps)
4.23 Convert 2 . 4 to a percent.
Move the decimal point two places to the right:
2 . 4 = 240%
Answer: 240%.
Worked example (no skipped steps)
4.24 A battery level goes from 25% to 40%. Find the percent increase.
Change:
40 − 25 = 15
Divide by the original level:
15 = 0 . 6
25
Convert:
0 . 6 = 60%
Answer: the battery level increased by 60%.