The ratio of boys to girls is 3 to 2. If there are 12 boys, how many girls are there?

Question:

The ratio of boys to girls is {eq}3:2{/eq}.

If there are {eq}12 {/eq} boys, how many girls are there?

Ratio:

A ratio shows the relative comparison of two or more quantities. If the ratio of two quantities is given to be {eq}a:b {/eq} then the first quantity can be assumed to be {eq}ax {/eq} and the second quantity can be assumed to be {eq}bx {/eq} where {eq}x {/eq} is constant. We can use the given conditions to solve for {eq}x {/eq}.

Answer and Explanation:

The ratio of boys to girls in a classroom is {eq}3:2 {/eq}.

So we can assume that,

the number of boys = {eq}3x {/eq}

and the number of girls = {eq}2x {/eq}.

The number of boys = {eq}12 {/eq}.

So we set the number of boys equal to {eq}12 {/eq} and solve the equation:

$$3x=12\\[0.4cm] \text{Dividing both sides by 3}, \\[0.4cm] x=4 $$

Therefore, the number of girls = {eq}2x=2(4)= \boxed{\mathbf{8}} {/eq}.


Learn more about this topic:

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What is Ratio in Math? - Definition & Overview

from CAHSEE Math Exam: Help and Review

Chapter 10 / Lesson 14
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