How to find the percent of increase - Algebra 1

Reference number is the total points available

Relative difference is the second exam score minus the first

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 . .

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 .

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.

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.

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 .

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

Between 2004 and 2005, 65 people unenroll:

Basic subtraction shows us that the price of milk increased by $0.30. Now, all we need to do is find what percent $0.30 is of the original price, $2.52. We can do this through cross-multiplication.

If we set , then will represent the percentage increase and therefore the final answer.

Cross-multiplying yields , which gives .

Divide both sides by 2.52 to isolate x:

x = 11.9, which is closest to 12%.

Find the increase in students in nominal terms (below, in the numerator) and divide that by the base, which is the number of students in the first year.

Multiply the result from above by 100 to get the percent increase.

%

Note: to get the final answer to two decimal places, carry at least 4 decimal places from the first step of the calculation.

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).

To find the percentage increase, first find the difference in sales earnings.

Then, divide this by the sales earnings from the first year.

Finally, multiply this fraction by 100 to get the percentage increase.

To find the percentage of increase, you must divide the change in amount by the original amount. In this case, the change in amount or amount increased is $600 ($3,000 minus $2,400). The original amount is Ned's original salary, or $2,400. Thus, to find the percentage of increase of Ned's salary, you simply divide $600 by $2400: , which equals to 0.25 or 25%.

To find the percent change in two numbers, we can use the formula . In our case, our final value is 75, and our initial value is 50. Substituting our values into the equation, we get .

First, find the increase in the number of freshmen from last year to this year. Given that the percentage increase is 22% (0.22 in decimal form), you can find this increased number by multiplying the percentage by 1436

So the number of freshmen has increased by 316. Add this to the number of freshmen last year.

So the number of freshmen for this year is 1752.

To find the percent increase of two numbers, use the following formula:

where is the new number and is the original number. For this problem, our formula would look like this:

or .

For this question, the only difficult part is knowing what is meant by "percent of increase." With questions of this type, we need to know what part of the original whole was added to yield the new, increased value. Here, the original value was 64 and the increased value is 88. First, we find the difference between the two:

This is the amount of increase. Next, we take , which is our percent of increase in fraction form. The simplified value of this number is , or .

The original number increased by 37.5%.

Lucy had $100 and then earned $10. Since her amount of money went up by $10, and 10 is 10% of 100, then her percent increase is 10%.

Also we can use the formula,