How to Solve Word Problems Involving Ratio Part 3

By | September 12, 2015

In the previous two posts, we have learned how to solve word problems involving ratio with two and three quantities. In posts, we are going to learn how to solve a slightly different problem where both numbers are increased.

Problem

The ratio of two numbers is 3:5 and their sum is 48. What must be added to both numbers so that the ratio becomes 3:4?

Solution and Explanation

First, let us solve the first sentence. We need to find the two numbers whose ratio is 3:5 and whose sum is 48.

Now, let x be the number of sets of 3 and 5.

3x + 5x = 48
8x = 48
x = 6

Now, this means that the numbers areĀ 3(6) = 18 and 5(6) = 30.

Now if the same number is added to both numbers, then the ratio becomes 3:4.

Recall that in the previous posts, we have discussed that ratio can also be represented by fraction. So, we can represent 18:30 as \frac{18}{30}. Now, if we add the same number to both numbers (the numerator and the denominator), we get \frac{3}{4}. If we let that number y, then

\dfrac{18 + y}{30 + y} = \dfrac{3}{4}.

Cross multiplying, we have

4(18 + y) = 3(30 + y).

By the distributive property,

72 + 4y = 90 + 3y

4y - 3y = 90 - 72

y = 18.

So, we add 18 to both the numerator and denominator of \frac{18}{30}. That is,

\dfrac{18 + 18}{30 + 18} = \dfrac{36}{48}.

Now, to check, is \dfrac{36}{48} = \frac{3}{4}? Yes, it is. Divide both the numerator and the denominator by 12 to reduce the fraction to lowest terms.

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2 thoughts on “How to Solve Word Problems Involving Ratio Part 3

    1. Civil Service Reviewer Post author

      Hello.

      Kasi yun ang greatest common denominator ng 36 and 48.

      Reply

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