Lesson 2-7

Example 1     Find Percent of Change
State whether each percent of change is a percent of increase or a percent of decrease. Then find each percent of change.
a.  	original: 18	b.	original: 125
		new: 18.99		new: 106.25
		Find the amount of change. Since the		The percent of change is a percent of 
		new amount is greater than the 		decrease because the new amount is
		original, the percent of change is a 		less than the original. Find the 
		percent of increase.		change.
		18.99 - 18 = 0.99		125 – 106.25 = 18.75
		Find the percent using the original		Find the percent using the original
		number, 18, as the base.		number, 125, as the base.

change

original amount

change

original amount

				 = 		 = 
		 0.99(100) = 18r			 18.75(100) = 125(r)
		99 = 18r		 1875 = 125r
		 = 		  = 
		 5.5 = r		 15 = r
		The percent of increase is 5.5%.		The percent of decrease is 15%.

Example 2     Find the Missing Value
JOBS    Due to hard times at his company, Jared was told that his salary would be cut by 10%.  If Jared was making $62,000, what will his new salary be?					
	
Let s = salary after 10% decrease. Since 10% is a percent of decrease, the new salary is less than the old salary. Therefore, 62,000 – s represents the amount of change.

change

original amount

	   = 	Percent proportion
	(62,000 – s)(100) = 62,000(10)	Find the cross products.
	6,200,000 – 100s = 620,000	Distributive Property
	6,200,000 – 100s – 6,200,000 = 620,000 – 6,200,000	Subtract 6,200,000 from each side.
		  -100s = -5,580,000	Simplify.
		  = 	Divide each side by –100.
	  s = 55,800	Simplify.
Jared’s new salary will be $55,800.

Real-World EXAMPLE
Example 3      Find Amount After Sales Tax
SALES TAX   A mountain bike costs $675. If the sales tax is 5.25%, what is the total price of the bike?
The tax is 5.25% of the price of the bike.
5.25% of $675 = 0.0525  675	5.25% = 0.0525
			 = 35.4375	Use a calculator.

Round $35.4375 to $35.44 since tax is always rounded up to the nearest cent.
Add this amount to the original price.

$675 + $35.44 = $710.44
The total price of the mountain bike is $710.44.

Example 4     Find Amount After Discount
DISCOUNT	A magazine costs $52 a year if you buy it every week off the newsstand. If you buy a subscription, you can buy it at a 15% discount, what is the discounted price?
	
The discount is 15% of the original price.
15% of $52 = 0.15  52	15% = 0.15
			= 7.8		Use a calculator.
Subtract $7.80 from the original price.
$52.00 - $7.80 = $44.20
The discounted price of the magazine subscription is $44.20.