Solving Proportion Problems

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.

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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.

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.

However, the unknown quantity was different for each problem. Red is used for the unknown quantity in each problem.

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.

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.In previous lessons, you were shown how to convert a decimal to a percent and a percent to a decimal.Thus, if you were asked to Find 15% of 120, you would multiply .15 by 120, to get an answer of 18.52 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.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.PERCENT is the unknown quantity in our proportion, to be represented by n.Substitute: becomes Solve: Cross multiply and we get: 56n = 14(100), or 56n = 1400 Divide both sides by 56 and we get: n = 25 Solution: 25% of 56 is 14 Problem 6: 18 is 75% of what number?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?Analysis: In this problem, you are being asked 8 is what percent of 20?

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