Using Proportions To Solve Problems

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

You are given two numbers from the proportion above and 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.

Note that in all three percent statements, the whole always follows the word "of" and the part always precedes the word "is".

We could have used equivalent fractions instead (i.e., since 20 multiplied by 5 equals 100, we get that 8 multiplied by 5 equals x, so x equals 40).

In Problem 1 we were asked 8 is what percent of 20?

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  1. This new collaboration extends the work started in 2014, when EBSCO and the H. Wilson Foundation created American Doctoral Dissertations which contained indexing from the H. Wilson print publication, Doctoral Dissertations Accepted by American Universities, 1933-1955.