## 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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The correct answer is B.

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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