Algebra 1 : How to find the percent of increase

Study concepts, example questions & explanations for Algebra 1

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Example Questions

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Example Question #1 : How To Find The Percent Of Increase

What is the percent of increase from 2000 to 2500? 

Possible Answers:

30%

25%

20%

10%

15%

Correct answer:

25%

Explanation:

2500 – 2000 = 500

The amount of increase is 500. The percent increase is found by dividing the amount increase by the original amount (2000).

500/2000 = 25/100 = 25%

Example Question #2 : How To Find The Percent Of Increase

A number is increased by 25%, giving the result of 16.  What is that number?

Possible Answers:

Correct answer:

Explanation:

Begin by translating your sentence into an equation.  The original number can be given the value "."  When you increase that number by , you can write it one of two ways:

Way 1: 

Way 2: 

Note that the second equation is merely a simplification of the first.  Now, just divide both sides by  to get . .

Example Question #3 : How To Find The Percent Of Increase

The volume of a balloon increases from 450 cubic centimeters to 575 cubic centimeters.  To the nearest whole number, what is the percentage increase in volume?

Possible Answers:

Correct answer:

Explanation:

To find the percentage difference, you merely subtract the start value from the end value and divide by the start.  The absolute change was  cubic centimeters or  cubic centimeters.  Divide this by the start value, , and you get  or .

Example Question #4 : Percent Of Change

A company loses $4 per sale of an item that is retailing for $18.  To the nearest hundredth, what percentage must it be marked up to break even?

Possible Answers:

Correct answer:

Explanation:

The product must make another  in order to break even.  Therefore, it must be marked up to a total price of .  The question is really asking for a percentage change.  The percentage change from  to  is:

.  NOTE: It must be marked up at least slightly more than 22.22% in order to break even.

Example Question #4 : How To Find The Percent Of Increase

After losing six pounds of body fat, Sam is 145 pounds with a body fat percentage of 18%.  What was the original weight of her body fat?

Possible Answers:

Correct answer:

Explanation:

If Sam is  lbs with a body fat percentage of , this means that she has of body fat.  Before losing the weight, she would have had  of body fat.

Example Question #5 : How To Find The Percent Of Increase

After losing 12 pounds of body fat, Pat weighs 157 pounds with a body fat percentage of 21%.  To the nearest hundredth, what was his original body fat percentage?

Possible Answers:

Correct answer:

Explanation:

If Pat is  lbs. with  body fat, he has  lbs. of body fat.  

When he was  lbs. heavier, he weighed  (that is, ) lbs., and would have had  (that is, ) lbs. of body fat on his body.  

This would mean that his body fat percentage is  or approximately .

Example Question #6 : How To Find The Percent Of Increase

2,800 is increased by 8%: What is the new number?

Possible Answers:

Correct answer:

Explanation:

Example Question #7 : How To Find The Percent Of Increase

There are 3000 people enrolled in a specific program in 2003. Between 2003 and 2004, the number of people enrolled increases by 12%, and between 2004 and 2005, 65 people unenroll. How many people are enrolled at the beginning of 2005?

Possible Answers:

Correct answer:

Explanation:

Between 2003 and 2004, the number of people enrolled increases by 12%:

Between 2004 and 2005, 65 people unenroll:

Example Question #8 : How To Find The Percent Of Increase

Possible Answers:

Correct answer:

Explanation:

Example Question #9 : How To Find The Percent Of Increase

An item is $20 and has its price increased by 10%.  It is then increased by 20% more.  What is the total percentage increase?

Possible Answers:

2%

22%

26.4%

32%

30%

Correct answer:

32%

Explanation:

Do not overthink this question.  Remember that if you have consecutive increases in value, you can multiply them in a row.  For instance, if you increase something costing  dollars by 50% and then again by 50%, you merely multiply twice by 1.5:

For our data, this would be:

Note that we DO NOT want to multiply everything out.  Instead, we can see immediately that we have 132% of 20 as the new value.  This means that it has been increased by 32% from its original price ($20).

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