Problem Solving With Percents

Every statement of percent can be expressed verbally as: "One number is some percent of another number." Percent statements will always involve three numbers. Thus the statement, "One number is some percent of another number.", can be rewritten: "One number is some percent of another number.", becomes, "The part is some percent of the whole." From previous lessons we know that the word "is" means equals and the word "of" means multiply.

Thus, we can rewrite the statement above: The statement: "The part is some percent of the whole.", becomes the equation: the part = some percent x the whole Since a percent is a ratio whose second term is 100, we can use this fact to rewrite the equation above as follows: the part = some percent x the whole becomes: the part = x the whole Dividing both sides by "the whole" we get the following proportion: Since percent statements always involve three numbers, given any two of these numbers, we can find the third using the proportion above. Problem 1: If 8 out of 20 students in a class are boys, what percent of the class is made up of boys?

The part is the unknown quantity and will be represented by p in our proportion.

becomes Solve: Cross multiply and we get: 100p = 52(25) or 100p = 1300 Divide both sides by 100 to solve for p and we get: p = 13 Solution: 13 is 25% of 52 Note that we could restate this problem as, "Find 25% of 52", and get the same answer.

14 is the part and will replace IS in our proportion.

PERCENT is the unknown quantity in our proportion, to be represented by n.

This is not surprising since our original statement is, "One number is some percent of another number." Thus, we can revise our proportion as follows: becomes Let's solve some more percent problems using proportions. Identify: 25% means that 25 will replace PERCENT in our proportion.

52 is the whole and will replace OF in our proportion.

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