## The Ratio Word Problems Tutorial Series

This is a series of tutorials regarding ratio word problems. Ratio is defined as the relationship between two numbers where the second number is how many times the first number is contained. In this series of problems, we will learn about the different types of ratio word problems.

How to Solve Word Problems Involving Ratio Part 1 details the intuitive meaning of ratio.  It uses arithmetic calculations in order to explain its meaning. After the explanation, the algebraic solution to the problem is also discussed.

How to Solve Word Problems Involving Ratio Part 2 is a continuation of the first part. In this part, the ratio of three quantities are described. Algebraic methods is used as a solution to solve the problem.

How to Solve Word Problems Involving Ratio Part 3 in this post, the ratio of two quantities are given. Then, both quantities are increased resulting to another ratio.

How to Solve Word Problems Involving Ratio Part 4 involves the difference of two numbers whose ratio is given.

If you have more math word problems involving ratio that are different from the ones mention above, feel free to comment below and let us see if we can solve them.

## 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 involving 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.

## How to Solve Word Problems Involving Ratio Part 1

In a dance school, 18 girls and 8 boys are enrolled. We can say that the ratio of girls to boys is 18:8 (read as 18 is to 8). Ratio can also be expressed as fraction so we can say that the ratio is 18/8. Since we can reduce fractions to lowest terms, we can also say that the ratio is 9/4 or 9:4. So, ratio can be a relationship between two quantities. It can also be ratio between two numbers like 4:3 which is the ratio of the width and height of a television screen.

Problem 1

The ratio of boys and girls in a dance club is 4:5. The total number of students is 63. How many girls and boys are there in the club?

Solution and Explanation

The ratio of boys is 4:5 means that for every 4 boys, there are 5 girls. That means that if there are 2 groups of 4 boys, there are also 2 groups of 5 girls. So by calculating them and adding, we have

4 + 5 = 9
4(2) +5(2) =18
4(3) +5(3) =27
4(4) +5(4) = 36
4(5) +5(5) = 45
4(6) +5(6) =54
4(7) +5(7) =63

As we can see, we are looking for the number of groups of 4 and, and the answer is 7 groups of each. So there are 4(7) = 28 boys and 5(7) = 35 girls.

As you can observe, the number of groups of 4 is the same as the number of groups of 5. Therefore, the question above is equivalent to finding the number of groups (of 4 and 5), whose total number of persons add up to 63.

Algebraically, if we let x be the number of groups of 4, then it is also the number of groups of 5. So, we can make the following equation.

4 x number of groups + 5 x number of groups of 5 = 63

Or

4x + 5x = 63.

Simplifying, we have

9x = 63
x = 7.

So there are 4(7) = 28 boys and 5(7) = 35 girls. As we can see, we confirmed the answer above using algebraic methods.