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Percent Change
% Change Word Problems
100

Change to a percent to a fraction: 50%

What is 1/2?

100

Change to a percent: 0.75

What is 75%?

100

Find the percent change. 

Original cost: $100 

New cost: $59

(59-100)/100 = -41/100 = -.41= -41% 

41% decrease

100

The price of gasoline rose from $3.50 to $3.71 in one week. By what percent did the gas price rise?

(3.71-3.50)/3.50 = .21/3.50= .06

6% increase

200

Change to a percent to a decimal: 10%

What is 0.10?

200

Change to a percent: 12/100

What is 12%?

200

Find the cost of the tickets after sales tax. 

tickets: $52.50

sales tax: 7%


54.5 * 107% = 54.5 *1.07 = $58.32

200

As soon as a new car is purchased and driven away from the dealership, it begins to lose its value, or depreciate. Alonso bought a 1994 Plymouth Neon for $9559. One year later, the value of the car was $8500. What was the percent of decrease of the value of the car?

(8500-9559)/8500 = -1059/8500 = -.12

12% decrease

300

Write the percent as a decimal: 125%

What is 1.25?

300

Change to a percent: 0.325

What is 32.5%?
300

Find the cost of the jeans after the discount.

jeans: $39.99 sales

discount: 15%

39.99 * (100%-15%) = 39.99 * 85% = 39.99 *.85 = $34

300

In 1995, America Online had about 3,000,000 users. Over the next decade, users are expected to increase from a few million to the tens of millions. Suppose the number of users increases by 150% by the year 2000. How many users will there be in the year 2000?

3,000,000 *1.5 = 4,500,000 users

400

Write the percent as a decimal: 6%

What is 0.06?

400

Change to a percent: 2/5

What is 40%?

400

What is the cost of the skates after the discount and tax are applied?

skates: $99.99

discount: 20%

sales tax: 6.75%

99.99 * (100%-20%) = 99.99 *80% = 99.99 *.8 = 80

80 * (100% + 6.75%) = 80 * 106.75% = 80 *1.0675 = 85.4

400

Music Systems, Inc. allows a 10% discount if a purchase is paid for within 30 days. An additional 5% discount is given if the purchase is paid for within 15 days. Brent Goodson buys a sound system that originally cost $360. If he pays the entire amount at the time of purchase, how much does he pay for his system after the successive discounts?

360* (100%-10%) = 360 *90% = 360 *.9 =324

324 * (100%-5%) = 324 *95% = 324 *.95= 307.80

500

Write the percent as a decimal: 503%

What is 5.03?

500

Change to a percent: 0.045

What is 4.5%?

500

What is the final cost of the book after the discount and tax?

book: $19.95 

discount: 5%

sales tax: 5%

19.95 *(100%-5%) = 19.95 *95% = 19.95 *.95 = 18.96

18.96 * (100% + 5%)= 18.96 * 105% = 18.96 *1.05 =  19.91

$19.91

500

A number is increased by 25% and the resulting number is then decreased by 20%. The final number is what percent of the original number?

A. 90%

B. 95%

C. 100%

D. 105%

E. 120%

(x * (100%+25%)) *(100% - 20%) =

(x * (125%)) *(80%) =

(x * (1.25)) *(.8) =1.25x * .8 = 1x 

1 = 100/100 = 100%

C