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The average heights of x number of girls and 15 boys is 123. if the average heights of boys is 125 and that of girls is 120.find number of girls.​

User JaggerJo
by
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1 Answer

6 votes

Answer:


x = 10. In other words, there number of girls is
10.

Explanation:

The average of a number of measurements is equal to the sum of these measurements over the number of measurements.


\displaystyle \text{Average} = \frac{\text{Sum of measurements}}{\text{Number of measurements}}.

Rewrite to obtain:


\begin{aligned}& \text{Sum of measurements}= (\text{Number of measurements}) * (\text{Average}) \end{aligned}.

For this question:


\begin{aligned}& \text{Sum of heights of boys} \\ &= (\text{Number of boys}) * (\text{Average height of boys}) \\ &= 15 * 125 = 1875\end{aligned}.


\begin{aligned}& \text{Sum of heights of girls} \\ &= (\text{Number of girls}) * (\text{Average height of girls}) \\ &= x * 120 = 120\, x\end{aligned}.

Therefore:


\begin{aligned}& \text{Sum of boys and girls} \\ &= \text{Sum of heights of boys} + \text{Sum of heights of girls}\\ &= 1875 + 120\, x\end{aligned}.

On the other hand, there are
(15 + x) boys and girls in total. Using the formula for average:


\begin{aligned}& \text{Average height of boys and girls} \\ &= \frac{\text{Sum of heights of boys and girls}}{\text{Number of boys and girls}} \\ &= (1875 + 120\, x)/(15 + x)\end{aligned}.

From the question, this average should be equal to
123. In other words:


\displaystyle (1875 + 120\, x)/(15 + x) = 123.

Solve this equation for
x to obtain:


1875 + 120\, x= 123\, (15 + x).


(123 - 120)\, x = 1875 - 123 * 15.


x = 10.

In other words, the number of girls here is
10.

User Linora
by
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