holt ca course 1 6-5 solving percents problems ns1.4 calculate given percentages of quantities and...
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Holt CA Course 1
6-5 Solving Percents Problems
NS1.4 Calculate given percentages of quantities and solve problems involving discounts at sales, interest earned, and tips.Also covered: NS1.3, AF1.1
California Standards
Holt CA Course 1
6-5 Solving Percents Problems
Sloths sleep an average of 16.5 hours a day. To find out what percent of a 24-hour day 16.5 hours is, you can use a proportion or an equation.
Holt CA Course 1
6-5 Solving Percents Problems
Proportion Method Equation Method
n100
= 16.524
PartWhole
PartWhole
What percent of 24 is 16.5?
n · 24 = 100 · 16.5
24n = 1,650
n = 68.75
n · 24 = 16.5
n = 0.6875
n = 68.75%
Sloths spend about 69% of the day sleeping!
Holt CA Course 1
6-5 Solving Percents Problems
Solve.
Additional Example 1: Using Proportions to Solve Problems with Percents
A. What percent of 40 is 25?n
100= 25
40
n · 40 = 100 · 25
40n = 2,500
40n40
= 2,500 40
n = 62.5
25 is 62.5% of 40.
Write a proportion.
Set the cross products equal.
Multiply.
Divide each side by 40.
Holt CA Course 1
6-5 Solving Percents Problems
Solve.
Additional Example 1: Using Proportions to Solve Problems with Percents
B. 15 is 25% of what number?
25100
= 15n
n · 25 = 100 · 15
25n = 1,500
25n25
= 1,500 25
n = 60
15 is 25% of 60.
Write a proportion.
Set the cross products equal.
Multiply.
Divide each side by 25.
Holt CA Course 1
6-5 Solving Percents Problems
Solve.
Check It Out! Example 1
A. What percent of 50 is 10?n
100= 10
50
n · 50 = 100 · 10
50n = 1,000
50n50
= 1,000 50
n = 20
10 is 20% of 50.
Write a proportion.
Set the cross products equal.
Multiply.
Divide each side by 50.
Holt CA Course 1
6-5 Solving Percents Problems
Solve.
Check It Out! Example 1
B. 8 is 40% of what number?
40100
= 8n
n · 40 = 100 · 8
40n = 800
40n40
= 800 40
n = 20
8 is 40% of 20.
Write a proportion.
Set the cross products equal.
Multiply.
Divide each side by 40.
Holt CA Course 1
6-5 Solving Percents Problems
Solve.
Additional Example 2: Using Equations to Solve Problems with Percents
A. 35 is 28% of what number?
35 = 28% · n
35 = 0.28 · n
350.28
= 0.28 · n0.28
125 = n
35 is 28% of 125.
Write an equation.
Write 28% as a decimal.
Divide each side by 0.28.
Holt CA Course 1
6-5 Solving Percents Problems
Solve.
Additional Example 2: Using Equations to Solve Problems with Percents
B. What percent of 9 is 18?
18 = n · 9
189
= n · 99
2 = n
200% = n
18 is 200% of 9.
Write an equation.
Divide each side by 9.
Write the decimal as a percent.
Holt CA Course 1
6-5 Solving Percents Problems
Solve.
Check It Out! Example 2
A. 36 is 24% of what number?
36 = 24% · n
36 = 0.24 · n
150 = n
36 is 24% of 150.
Write an equation.
Write 24% as a decimal.
Divide each side by 0.24.360.24
= 0.24 · n0.24
Holt CA Course 1
6-5 Solving Percents Problems
Solve.
Check It Out! Example 2
B. What percent of 6 is 36?
36 = n · 6
366
= n · 66
6 = n
600% = n
36 is 600% of 6.
Write an equation.
Divide each side by 6.
Write the decimal as a percent.
Holt CA Course 1
6-5 Solving Percents Problems
A portable DVD player costs $225 before tax at an appliance warehouse. What is the sales tax rate if the tax is $18?
Additional Example 3: Finding Sales Tax
n100
= 18225
n · 225 = 100 · 18
8% of $225 is $18. The sales tax is 8%.
Write a proportion.
Set the cross products equal.
Multiply.
Restate the question: What percent of $225 is $18?
225n = 1800
225n225
= 1800225
Divide each side by 225.
n = 8
Holt CA Course 1
6-5 Solving Percents Problems
Helpful Hint
The sales tax rate is the percent used to calculate sales tax.
Holt CA Course 1
6-5 Solving Percents Problems
A new flat screen TV costs $800 before tax at an appliance warehouse. What is the sales tax rate if the tax is $56?
Check It Out! Example 3
n100
= 56800
n · 800 = 100 · 56
7% of $800 is $56. The sales tax is 7%.
Write a proportion.
Set the cross products equal.
Multiply.
Restate the question: What percent of $800 is $56?
800n = 5600
800n800 =
5600 800
Divide each side by 800.
n = 7