Solving Ratio Problems Involving Totals

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  • 0:04 Ratio Problems
  • 1:16 Ration Problems…
  • 3:59 Another Examples
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Lesson Transcript
Instructor: Laura Pennington

Laura has taught collegiate mathematics and holds a master's degree in pure mathematics.

A brief review of what ratios are will be given, and then we will look at ratio problems involving totals. We will look at the steps involved in solving these types of problems using various examples.

Ratio Problems

Let's suppose you're comparing the number of men to women at a particular college, and in doing so, you find that for every nine women there are eight men. Guess what? You actually just discovered the ratio of women to men at the college, and that is 9 to 8.

A ratio is a comparison of two amounts. When you found the ratio of women to men at the college, you were comparing the number of women to men. To indicate a ratio of a to b, we use the following notations:

  • a to b
  • a : b
  • a / b

For example, the ratio of women to men at the college can be written as follows.

  • 9 to 8
  • 9 : 8
  • 9 / 8

Are you with me so far? Good, let's talk problems - ratio problems, that is! In mathematics, any problems involving ratios are called ratio problems. These types of problems can be solved using proportions, where a proportion is an equation of two ratios set equal to one another. In a ratio problem, we want to set up a proportion with the information given and then solve the proportion for the unknown quantity using cross multiplication.


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We see that if we have a proportion a / b = c / d, then ad = bc. This fact will come in very handy when solving ratio problems.

Ratio Problems Involving Totals

Sometimes ratio problems involve calculating totals in order to solve the problem. This is usually indicated when the problem gives a ratio and a total. For example, consider the college again, and suppose we are told that the ratio of women to men is 9 to 8, and there are a total of 5,644 students at the college. We want to find how many women attend the college. Notice that this problem gives the ratio and then tells how many total students are at the college indicating that it's a ratio problem involving totals.

In general, when dealing with ratio problems involving totals, we can use a ratio box to organize and solve the problem. A ratio box has columns of ratio and actual amount and rows of the variables involved in the ratio, along with a third row of totals.


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To solve ratio problems involving totals, we take these steps:

  1. Name the unknowns using variables.
  2. Set up a ratio box with totals using the given information.
  3. Use the ratio box to set up a proportion.
  4. Solve the proportion using cross multiplication.

Okay, that's a lot of information all at once! Let's take our college ratio problem involving totals through these steps to help us better understand the solving process.

We are given that the ratio of women to men at the college is 9 to 8 and that the total number of students at the college is 5,644. We don't know the actual count of women or the actual count of men at the college, so let's represent those values as w and m, respectively. Alright! We're ready to set up our ratio box! Our columns will be ratio and actual amount, and our rows will be women, men, and totals.


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Now we just need to fill it in with the information that we know!


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