How to Solve Word Problems Involving Ratio Part 4

This is the fourth and the last part of the solving problems involving ratio series. In this post, we are going to solve another ratio word problem.

Problem

The ratio of two numbers 1:3. Their difference is 36. What is the larger number?

Solution and Explanation

Let x be the smaller number and 3x be the larger number.

3x – x = 36
2x = 36
x = 18

So, the smaller number is 18 and the larger number is 3(18) = 54.

Check:

The ratio of 18:54 is 1:3? Yes, 3 times 18 equals 54.
Is their difference 36? Yes, 54 – 18 = 36.

Therefore, we are correct.

How to Solve Word Problems Involving Ratio Part 2

This is the second part of a series of post on Solving Ratio Problems. In the first part, we have learned how to solve intuitively and algebraically problems involvingĀ ratio of two quantities. In this post, we are going to learn how to solve a ratio problem involving 3 quantities.

Problem 2

The ratio of the red, green, and blue balls in a box is 2:3:1. If there are 36 balls in the box, how many green balls are there?

Solution and Explanation

From the previous, post we have already learned the algebraic solutions of problems like the one shown above. So, we can have the following:

Let $x$ be the number of grous of balls per color.

$2x + 3x + x = 36$

$6x = 36$

$x = 6$

So, there are 6 groups. Now, since we are looking for the number of green balls, we multiply x by 3.

So, there are 6 groups (3 green balls per group) = 18 green balls.

Check:

From above, $x = 6(1)$ is the number of blue balls. The expression 2x represent the number of red balls, so we have 2x = 2(6) = 12 balls. Therefore, we have 12 red balls, 18 green balls, and 6 blue balls.

We can check by adding them: 12 + 18 + 6 = 36.

This satisfies the condition above that there are 36 balls in all. Therefore, we are correct.