Big Ideas Math: Modeling Real Life, Grade 7
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2. The Percent Proportion
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Exercise 31 Page 246

The percent proportion is a proportion that equates a part of a whole to a percent out of 100.

8.4

Practice makes perfect
We are told that our friend earns $10.50 per hour this year which is 125% of her last year's hourly wage. We can find what number's 125% is equal to $10.50 to find her last year's hourly wage. Recall that the percent proportion is a proportion that sets the ratio of a part of a whole equal to the ratio of a percent out of 100. We can represent a is p percent of wwith the given proportion. part/whole=percent/100 ⇔ a/w=p/100We can find what number's 125% is $10.50 by thinking about 125 as the percent and 10.5 as a part of the whole. Let's substitute a= 10.5 and p= 125 into the formula and solve for w using the Properties of Equality.
a/w=p/100
10.5/w=125/100
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Solve for p
10.5/w* w=125/100 * w
10.5=125/100 * w
10.5=125w/100
10.5* 100=125w/100* 100
10.5* 100=125w
1050=125w
1050/125=w
8.4=w
w= 8.4
Knowing the value of w, let's look at the completed percent proportion. 10.5/8.4=125/100 We found that 10.5 is 125 % of 8.4.