The ratio of boys to girls in a room is 6:5. If three boys leave the room, the ratio is 1:1. How...

Question:

The ratio of boys to girls in a room is {eq}6:5 {/eq}. If three boys leave the room, the ratio is {eq}1:1 {/eq}. How many girls are in the room?

Ratio:

A ratio shows the relative comparison of two or more quantities. A ratio {eq}a:b {/eq} can be written as a fraction {eq}\dfrac{a}{b} {/eq} and in turn, a fraction {eq}\dfrac{a}{b} {/eq} can be written as a ratio {eq}a:b {/eq}.

Answer and Explanation:

The problem says, "The ratio of boys to girls in a room is 6:5".

So we can assume the number of boys to be {eq}6x {/eq}

and the number of girls to be {eq}5x {/eq}.

Now three boys left the room.

So the current number of boys = {eq}6x-3 {/eq}.

Since no girls left the room, the current number of girls = {eq}5x {/eq}.

The new ratio is {eq}1:1 {/eq}.

So we get:

$$\dfrac{6x-3}{5x}= \dfrac{1}{1} \\[0.4cm] \text{Multiply both sides by 5x}, \\[0.4cm] 6x-3 = 5x \\[0.4cm] \text{Subtracting 5x from both sides}, \\[0.4cm] x-3=0 \\[0.4cm] \text{Adding 3 on both sides}, \\[0.4cm] x=3 $$

Therefore, the number of gilrs = {eq}5x = 5(3) = \boxed{\mathbf{15}} {/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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