Ratio, Proportion and Percentages Puzzle – Challenge 24

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=-80end{cases} Rightarrow begin{cases}8x-3y = -80\ -16x+6y=160end{cases})
From the system of equations above: (x = 32) and (y = 112)
32 girls are currently attending the school.

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