More Percent Problems Answers

 “Successive Percentage Changes”

--An item costs $120.  It is on sale for 25% off.  You have a coupon for an additional 10% off. 

What is the final sale price of the article?

120*(1-.25) = 90

90 *(1-.1) = 81

The final sale price was $81.

How much do you save overall?

120-81 = 39

You save a total of $39.

What is the overall percent savings?

(81-120)/120 = 32.5%

You save 32.5% overall.

 --A retail store buys items from the manufacturer and then marks up the price 75%.  During a sale, prices are discounted 25%.  The store makes what percent profit? 

If no original value is given, use 100.

100 * (1+.75) = 175

175 * (1-.25) = 131.25

(131.25-100)/100 = 31.25 %

 

--Spot prices for crude oil are rather volatile.  From 1998 to 1999, spot prices for crude oil decreased by 28%.  From 1999 to 2000, they increased by 106%.  What was the percentage change over the two year period from 1998 to 2000?

If no original value is given, use 100.

 100 *(1-.28) = 72

72 * (1+1.06) = 148.32

 (148.2-100)/100 = 48.2%

The overall percent change was 48.2%

 

“Reverse Percentage Change”

--During a 25% off sale, you buy an item for $22.50.  What was the original price of the item?

For a reverse percent change use N= P * (1 + r) or  N= P * (1 - r) but the original value (P) is unknown.

22.50 = P * (1-.25)

22.50 = .75 P

P = 30

The original price was $30.00.

Note:  You CANNOT increase 22.50 by 25% to get the correct answer.

--In 2004, the number of new hybrid vehicle registrations was 83,153 which is an 81% increase over the previous year.   How many hybrid vehicle registrations were there in 2003?

For a reverse percent change use N= P * (1 + r) or  N= P * (1 - r) but the original value (P) is unknown.

83,153 = P * (1+.81)

83,153 = 1.81P

P = 45941

There were 45,941 hybrid vehicles registered in 2003.

--According to the official 2000 census, the Hispanic population of the US in 2000 was 35,306,000.  The population had risen an astounding 57.9% from 1990 to 2000.  What was the Hispanic population in 1990?

For a reverse percent change use N= P * (1 + r) or  N= P * (1 - r) but the original value (P) is unknown.

 35,306,000 = P * (1+.579)

35,306,000 = 1.579P

divide both sides by 1.579

P = 22359721

The Hispanic population in 1990 was 22,359,721.