1. Warm Up
Problem of the Day
Lesson Presentation
Lesson Quizzes

2. Warm Up
Solve.
1. 4x = 90
2. 8x = 96
3. 12x = 180
4. 26x = 182
22.5 12 15 7

3. Rearrange the digits in . What
Problem of the Day
Rearrange the digits in What
fraction of the possible arrangements are true proportions? 2 6 1 3 = 1 3

4. Sunshine State Standards
MA.7.A.1.2 Solve percent problems, including problems involving discounts…[and] taxes…

5. Sloths may seem lazy, but their extremely slow movement helps to make them almost invisible to predators. Sloths sleep an average of 16.5 hours a day. To find out what percent of a 24-hour day hours is, you can use a proportion or an equation.

6. Proportion Method Equation Method
Part n
16.5
Part =
What percent of 24 is 16.5?
Whole
100 24
Whole
n · 24 = 100 · 16.5
n · 24 = 16.5
24n = 1,650
n =
n = 68.75
n = 68.75%
Sloths spend about 69% of the day sleeping!

7. Additional Example 1A: Using Proportions to Solve Problems with Percents
What percent of 40 is 25? n
100 = 25 40
Write a proportion.
n · 40 = 100 · 25
Set the cross products equal.
40n = 2,500
Multiply.
40n 40
= 2,500 40
Divide each side by 40 to isolate
the variable.
n = 62.5
25 is 62.5% of 40.

8. Additional Example 1B: Using Proportions to Solve Problems with Percents
15 is 25% of what number? 25
100 = 15 n
Write a proportion.
n · 25 = 100 · 15
Set the cross products equal.
25n = 1,500
Multiply.
25n 25
= 1,500 25
Divide each side by 25 to isolate
the variable.
n = 60
15 is 25% of 60.

9. Check It Out: Example 1A
Find the percent of each number.
What percent of 320 is 40? n
100 = 40
320
320n = 4,000
12.5 = n
12.5%

10. Check It Out: Example 1B
Find the percent of each number.
8 is 40% of what number? 8 n 40
100 =
40n = 800
n = 20 20

11. Additional Example 2A: Using Equations to Solve Problems with Percents
35 is 28% of what number?
35 = 28% · n
Write an equation.
35 = 0.28 · n
Write 28% as a decimal. 35
0.28
0.28 · n
0.28
Divide each side by 0.28 to isolate the variable. =
125 = n
35 is 28% of 125.

12. Additional Example 2B: Using Equations to Solve Problems with Percents
What percent of 9 is 18?
18 = n · 9
Write an equation. 18 9
n · 9 9
Divide each side by 9 to isolate the variable. =
2 = n
Write the decimal as a percent.
200% = n
18 is 200% of 9.

13. Check It Out: Example 2A
Solve.
9 is 75% of what number?
9 = 0.75 · n 9
0.75 =
0.75n
12 = n

14. Check It Out: Example 2B
Solve.
24 is 150% of what number?
14 = n 24
1.5
1.5n
1.5 =
16 = n

15. Additional Example 3: Consumer Application
Raoul found a pair of shoes that were marked down to 80% of the original price. He had a coupon that gave him an additional $10 off the shoes. The sales tax rate was 6.5% and Raoul paid $5.46 in sales tax. What was the original price of the pair of shoes?
Work backward. Find the final price of the shoes.
6.5% of price is $5.46.
Write a word sentence.
0.065  x = 5.46
Write an equation.
Divide both sides by
x = 84
The price of the shoes with the coupon was $84.

16. Additional Example 3 Continued
Find the price of the shoes without the coupon.
= 94
The price of the shoes was $94 after it was marked down to 80% of the original price. Find the original price.
80% of price is $94.
Write a word sentence.
0.8  x = 94
Write an equation.
Divide both sides by 0.8.
x = 117.5
The original price of the shoes was $

17. Check It Out: Example 3A
Marie-Claire bought a scarf marked down to 75% of its original price. She had a coupon that gave her an additional $5 off the scarf. The sales tax rate was 6%, and Marie-Claire paid $1.35 in sales tax. What was the original
price of the scarf?
Find the price before the sales tax was applied: = x
1.35
0.06
0.06x =
$22.50 = x

18. Check It Out: Example 3A Continued
Find the price before Marie used her $5 coupon: = $27.50
Find the price before the markdown: · x = 27.50
0.75x
0.75
27.50x
0.75 =
x = 36.67
The original price of the scarf was $36.67.

19. Check It Out: Example 3B
In 2008, Brenda made $42,756, which was 105% of what she made in In 2007, she made $4,000 more than she made in The amount she made in 2006 was 102% of what she made in How much did Brenda make in 2005?
Find what she made in 2007: ,756 = x
42,756
1.05
1.05x =
$40,720 = x

20. Check It Out: Example 3B Continued
Find what she made in 2006: 40,720 - $4,000 = $36,720
Find what she made in 2005: 36,720 = x
36,720x
1.02
1.02x
1.02 =
36,000 = x
Brenda made $36,000 in 2005.

21. Additional Example 4: Finding Sales Tax
A portable DVD player costs $225 before tax at an appliance warehouse. What is the sales tax rate if the tax is $18?
Restate the question: What percent of $225 is $18? n
100 18
225 =
Write a proportion.
n · 225 = 100 · 18
Set the cross products equal.
225n = 1800
Multiply.
225n
225
1800
225 =
Divide each side by 225.
n = 8
8% of $225 is $18. The sales tax is 8%.

22. Check It Out: Example 4A
Jarell paid $25.56 for his new bookbag. The amount he paid included a sales tax of $1.56. Find the sales tax rate. n
100 =
1.56 24
30n = 1.56(100)
The sales tax rate is 6.5%.
Price before sales tax: = $24
24n
156
n = 0.065

23. Check It Out: Example 4B
Lisa paid $11 sales tax for a bike. If the sales tax rate was 5.5%, how much did the bike cost without the sales tax?
11 = x
The bike cost $200 without sales tax. 11
0.055 =
0.055 x
200 = x

24. Lesson Quizzes
Standard Lesson Quiz
Lesson Quiz for Student Response Systems

25. Lesson Quiz
Solve.
1. 21 is 42% of what number?
2. What percent of 292 is 73?
3. 112% of what number is 84?
4. What percent of 1,340 is 13.4?
5. An ad features a bicycle on sale for $139. If the total cost of the bike is $147.34, what is the sales tax rate? 50
25% 75 1% 6%

26. Lesson Quiz for Student Response Systems
1. Solve. 19 is 38% of what number?
A. 69
B. 50
C. 38
D. 34

27. Lesson Quiz for Student Response Systems
2. What percent of 170 is 51?
A. 25%
B. 30%
C. 40%
D. 50%

28. Lesson Quiz for Student Response Systems
3. 128% of what number is 96?
A. 25
B. 50
C. 75
D. 96

29. Lesson Quiz for Student Response Systems
4. What percent of 1,520 is 15.2?
A. 25%
B. 15%
C. 10%
D. 1%

30. Lesson Quiz for Student Response Systems
5. A jeweler has a pendant on sale for $150. If the total cost of the pendant is $160.50, what is the sales tax rate?
A. 6%
B. 7%
C. 8%
D. 9%