11-4 Apply Percents to Algebraic Problems
Name
Date
Find the total cost of a $54.86 jacket after a 7.1% sales tax is added.
7.1% of $54.86
Find the sales tax.
Think
7.1
71
7.1% ⫽ 100 ⫽ 1000 ⫽ 0.071
0.071 • 54.86 ⫽ 3.89506
Write the percent as a decimal and multiply.
The sales tax rounded to the nearest cent is $3.90.
54.86 ⫹ 3.90 ⫽ 58.76
Find the cost of the jacket plus tax.
The total cost of the jacket plus tax is $58.76.
Solve each problem.
1. Find the sale price of a $15.95 book that
is discounted 20%.
0.2 • 15.95 ⴝ 3.19; 15.95 ⴚ 3.19 ⴝ 12.76
2. Find the sale price of a $36.10 tool that
is discounted 30%.
0.3 • 36.10 ⴝ 10.83; 36.10 ⴚ 10.83 ⴝ 25.27
$12.76
$25.27
3. Find the total cost of a $125.65 pair of boots
after an 8.5% sales tax is added.
0.085 • 125.65 艐 10.68; 125.65 ⴙ 10.68 ⴝ 136.33
0.075 • 102.38 艐 7.68; 7.68 ⴙ 102.38 ⴝ 110.06
$136.33
$110.06
5. Megan earns a 1.5% commission on her total
sales. One day her total sales were $6258.95.
How much was her commission?
6. Jeremiah earns a 2.5% commission on his total
sales. Last month his total sales were $186,915.
How much was his commission?
$93.88
$4672.88
0.015 • 6258.95 艐 93.88
Copyright © by William H. Sadlier, Inc. All rights reserved.
4. Find the total cost of a $102.38 pair of shoes
after a 7.5% sales tax is added.
7. Find the amount of simple interest $1500 would
earn in 4 years if deposited in an account that
paid 2.8% interest. (Hint: I ⫽ Prt)
1500 • 0.028 • 4 ⴝ 168
0.025 • 186,915 艐 $4672.88
8. Find the amount of simple interest $3100 would
earn in 3 years if deposited in an account that
paid 4.1% interest.
3100 • 0.041 • 3 ⴝ 381.3
$168
$381.30
9. Lionel was charged 6.1% simple interest on a
loan of $6000. He paid the money plus interest
after 3 years. How much did he pay altogether?
6000 • 0.061 • 3 ⴝ 1098; 1098 ⴙ 6000 ⴝ 7098
10. Melissa was charged 4.9% simple interest on a
loan of $8000. She paid the money plus interest
after 4 years. How much did she pay altogether?
8000 • 0.049 • 4 ⴝ 1568; 1568 ⴙ 8000 ⴝ 9568
$7098
$9568
11. Tony buys a $980 printer on sale for 25% off.
What is the total cost of the printer, including
a sales tax of 5.8% of the discounted price?
980 • 0.25 ⴝ 245; 980 ⴚ 245 ⴝ 735
735 • 0.058 ⴝ 42.63; 42.63 ⴙ 735 ⴝ 777.63
12. Maria buys a $1240 computer on sale for 40% off.
What is the total cost of the computer, including
a sales tax of 6.5% of the discounted price?
1240 • 0.4 ⴝ 496; 1240 ⴚ 496 ⴝ 744
744 • 0.065 ⴝ 48.36; 744 ⴙ 48.36 ⴝ 792.36
$777.63
$792.36
Lesson 11-4, pages 288–289.
Chapter 11 283
For More Practice Go To:
amount of change
Solve each problem. Show your work. (Hint: percent of change ⫽ original amount ⫻ 100)
13. Kirk’s starting wage was $12 per hour. One year 14. Jennifer’s starting wage was $15 per hour. One
later he earns $13.50 per hour. What is the
year later she earns $18.75 per hour. What is
percent of increase in his hourly wage?
the percent of increase in her hourly wage?
1.5
• 100 ⴝ 12.5%
12
18.75 ⴚ 15 ⴝ 3.75;
12.5%
25%
15. Lisa bought a boat for $34,850. She sold it three
years later for $23,698. What was the percent
of decrease in the value of the boat?
34,850 ⴚ 23,698 ⴝ 11,152;
11,152
• 100 ⴝ 32%
34,850
16. Janice bought a motorcycle for $12,900. She
sold it two years later for $5,805. What was the
percent of decrease in the value of the motorcycle?
12,900 ⴚ 5,805 ⴝ 7,095;
32%
17. Store A buys saws for $8.50 and sells them
for $21.25. Store B buys saws for $7.50 and
sells them for $20.25. Which store marks up
the saws more?
12.75
• 100 ⴝ 150%
8.5
12.75
Store B: 20.25 ⴚ 7.5 ⴝ 12.75;
• 100 ⴝ 170%
7.5
Store B marks-up the saws more.
Store A: 21.25 ⴚ 8.5 ⴝ 12.75;
19. Oscar bought a game that was discounted by
20%. To pay for the game plus a 10% sales
tax on the discounted price, he used a coupon
for $5 and gave the cashier $17. What was the
original price of the game?
Let x ⴝ price of game; y ⴝ discounted price
of game; x ⴚ 0.2x ⴝ y and y ⴙ 0.1y ⴝ total price.
So y ⴝ 0.8x and the total price is 1.1y. Now work
backward: 17 ⴙ 5 ⴝ 22, total price; 22 ⴜ 1.1 ⴝ 20,
price of game; 20 ⴜ 0.8 ⴝ 25, original price
The original price was $25.
21. Write a quadratic equation with roots 15 and 4.
(x ⴚ 15)(x ⴚ 4) ⴝ 0
x2 ⴚ 4x ⴚ 15x ⴙ 60 ⴝ 0
x2 ⴚ 19x ⴙ 60 ⴝ 0
284 Chapter 11
3.75
• 100 ⴝ 25%
15
7,095
• 100 ⴝ 55%
12,900
55%
18. Store A buys hats for $22 and sells them for $77.
Store B buys hats for $24 and sells them for $84.
Which store marks-up the hats more?
55
• 100 ⴝ 250%
22
60
Store B: 84 ⴚ 24 ⴝ 60;
• 100 ⴝ 250%
24
Both stores mark-up the hats equally.
Store A: 77 ⴚ 22 ⴝ 55;
20. Geometry Martina increased the length
and width of her rectangular garden by 15%.
By what percent is the area of her garden
increased? (Hint: A ⫽ ᐉw)
Use logical reasoning;
Area of original rectangle ⴝ ᐉw
Area of increased rectangle ⴝ (1.15w)(1.15ᐉ)
ⴝ 1.3225ᐉw
1.3225ᐉw ⴚ ᐉw ⴝ 0.3225ᐉw;
0.3225ᐉw ⴜ ᐉw ⴝ 0.3225 ⴝ 32.25%
The area of the garden increased by 32.25%.
22. What is the distance between point (9, 3) and
point (8, 2)?
dⴝ
( 9 ⴚ 8 )2 ⴙ ( 3 ⴚ 2 )2
dⴝ 2
Copyright © by William H. Sadlier, Inc. All rights reserved.
13.50 ⴚ 12 ⴝ 1.50;