All Algebra 1 Resources
Example Question #1 : Percent Of Change
What is the percent of increase from 2000 to 2500?
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 : Percent Of Change
A number is increased by 25%, giving the result of 16. What is that number?
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:
Note that the second equation is merely a simplification of the first. Now, just divide both sides by to get . .
Example Question #1 : 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?
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 #2 : How To Find The Percent Of Increase
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?
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 #5 : Percent Of Change
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?
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 #6 : Percent Of Change
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?
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 #3 : How To Find The Percent Of Increase
2,800 is increased by 8%: What is the new number?
Example Question #8 : Percent Of Change
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?
Between 2003 and 2004, the number of people enrolled increases by 12%:
Between 2004 and 2005, 65 people unenroll:
Example Question #9 : Percent Of Change
Example Question #4 : 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?
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).