# Problem Solving With Percents

We did this by letting a variable represent the unknown quantity and then substituting the given values into a proportion to solve for the unknown quantity.Note that in all three percent statements, the whole always follows the word "of" and the part always precedes the word "is".Thus, if you were asked to Find 15% of 120, you would multiply .15 by 120, to get an answer of 18.

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and how would we solve this problem: What is 20% of 45? 40% means that 40 will replace percent in our proportion.

The phrase of what number represents the whole and is the unknown quantity.

." If any two of the variables are given, you can use algebra to find out the missing one. In each one, the unknown is in a different position.

In previous lessons, you were shown how to convert a decimal to a percent and a percent to a decimal.

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.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?20% means that 20 will replace percent in our proportion. Substitute: Now we can substitute these values into our proportion.becomes Solve: Cross multiply and we get: 100x = 45(20) or 100x = 900 Divide both sides by 100 to solve for x and we get: x = 9 Solution: 9 is 20% of 45 In Problems 1, 2 and 3 we are given two numbers and asked to find the third by using a proportion.14 is the part and will replace IS in our proportion.PERCENT is the unknown quantity in our proportion, to be represented by n.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.becomes Solve: Cross multiply and we get: 40x = 18(100) or 40x = 1800 Divide both sides by 40 to solve for x and we get: x = 45 Solution: 18 is 40% of 45 Problem 3: What is 20% of 45?Identify: The phrase what is means represents the part and is the unknown quantity.

## Comments Problem Solving With Percents

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