2-9 Percents

Quick Review

A percent is a ratio that compares a number to 100. If you write a percent as a fraction, you can use a proportion to solve a percent problem.

Example

What percent of 84 is 105?

105 84 = p 100 Write the percent proportion . 100 ( 105 ) = 84 p Cross Products Property 10 , 500 = 84 p Simplify . 125 = p Divide each side by  84 . table with 4 rows and 3 columns , row1 column 1 , 105 over 84 , column 2 equals , p over 100 , column 3 cap writethepercentproportion . . , row2 column 1 , 100 . open 105 close , column 2 equals 84 p , column 3 cap crosscap productscap property , row3 column 1 , 10 comma 500 , column 2 equals 84 p , column 3 cap simplify , . , row4 column 1 , 125 , column 2 equals p , column 3 cap divideeachsideby . 84 . , end table

105 is 125% of 84.

Exercises

52. What percent of 37 is 111?
53. What is 72% of 150?
54. 60% of what number is 102?
55. Gardening A gardener expects that 75% of the seeds she plants will produce plants. She wants 45 plants. How many seeds should she plant?
56. Fundraising A charity sent out 700 fundraising letters and received 210 contributions in response. What was the percent of response?
57. Surveys In a survey, 60% of students prefer bagels to donuts. If 120 students were surveyed, how many students prefer bagels?

2-10 Change Expressed as a Percent

Quick Review

Percent change p% is the ratio of the amount of change to the original amount.

p % = amount of increase or decrease original amount p percent equals . fraction amountofincreaseordecrease , over originalamount end fraction

You can use the percent change formula to express changes as percents.

Example

A bookstore buys a book for $16 and marks it up to $28. What is the markup expressed as a percent change?

percent change = new amount − original amount original amount     = 28 − 16 16 Substitute .   = 12 16 Simplify .   = 0.75  or  75 % Write the result as a percent . table with 4 rows and 3 columns , row1 column 1 , percentchange , column 2 equals . fraction newamount . minus . originalamount , over originalamount end fraction , column 3 , row2 column 1 , , column 2 equals . fraction 28 minus 16 , over 16 end fraction , column 3 cap substitute . . , row3 column 1 , , column 2 equals , 12 over 16 , column 3 cap simplify , . , row4 column 1 , , column 2 equals , 0.75 , or , 75 percent , column 3 cap writetheresultasapercent . . , end table

The price of the book increased by 75%.

Exercises

Tell whether each percent change is an increase or decrease. Then find the percent change. Round to the nearest percent.

58. original amount: 27

    new amount: 30

59. original amount: 250

    new amount: 200

60. original amount: 873

    new amount: 781

61. original amount: 4.7

    new amount: 6.2

62. Demographics In 1970, the U.S. population was about 205 million people. In 2007, it was about 301 million. What was the percent increase?
63. Astronomy The time from sunrise to sunset on the shortest day of the year in Jacksonville, Florida, is about 10 h 11 min. On the longest day, the time is 14 h 7 min. What is the percent increase?
64. Weather This morning the temperature was 38°F. This afternoon it is 57°F. Did the temperature increase by 50%? Explain.

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