# Problem Solving With Percents

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However, in the interest of consistency, we will use proportions to solve percent problems throughout this lesson.

In Problems 5 through 7, we will use n to represent the unknown quantity. Identify: 56 is the whole and will replace OF in our proportion.

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.

In this problem, the percent is the unknown quantity! Looking at this problem, it is clear that 8 is the part and 20 is the whole.

We need to figure out how to find this unknown quantity. Similarly, in the statement, "One number is some percent of another number.", the phrase "one number" represents the part and "another number" represents the whole.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.But what would you do if you given this problem: 8 is what percent of 20?and we found the solution by substituting into a proportion.But how would we solve this problem: 18 is 40% of what number? Identify: The phrase 18 is means that 18 is the part.Analysis: In this problem, you are being asked 8 is what percent of 20?You are given two numbers from the proportion above and asked to find the third.We will let variable x represent this unknown quantity in our proportion.Substitute: Now we can substitute these values into our proportion.

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