Problem Solving Percentage

52 is the whole and will replace OF in our proportion.The part is the unknown quantity and will be represented by p in our proportion.Note that in all three percent statements, the whole always follows the word "of" and the part always precedes the word "is".

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But how would we solve this problem: 18 is 40% of what number? Identify: The phrase 18 is means that 18 is the part.

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

In Problem 1 we let x represent the unknown quantity "what percent"; in Problem 2 we let x represent the unknown quantity "of what number"; and in Problem 3 we let x represent the unknown quantity "What is." Thus, we solved three different percent problems, where in each problem, two numbers were given and we were asked to find the third.

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.

Identify: The phrase what is means represents the part and is the unknown quantity.

20% means that 20 will replace percent in our proportion. Substitute: Now we can substitute these values into our proportion.

You are given two numbers from the proportion above and asked to find the third.

The percent is the unknown quantity in this problem. Identify: The phrase 8 is means that 8 is the part.

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

We will let variable x represent this unknown quantity in our proportion.