Ratio, Proportion and Percentages Puzzle – Challenge 24

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Challenge:

The current ratio of girls to boys at a certain school is 2 to 7. If 10 additional girls were added to the school, the new ratio of girls to boys would be 3 to 8. How many girls currently attend the school?

A- 22

B- 32

C- 42

D- 56

E- 112

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Put x for the number of current girls and y for the number of current boys at the school. First, let’s set up our ratios.
$$\frac{x}{y} = \frac{2}{7}$$ and $$\frac{x+10}{y }= \frac{3}{8 }$$
Use cross multiplication to write the equations.
$$7x = 2y$$ and $$8 (x+10) = 3y ⇒ 8x + 80 = 3y$$
Now, we have a system of equations with two variables.
$$\begin{cases}7x-2y = 0\\ 8x-3y=-80\end{cases} \Rightarrow \begin{cases}8x-3y = -80\\ -16x+6y=160\end{cases}$$
From the system of equations above: $$x = 32$$ and $$y = 112$$
32 girls are currently attending the school.

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