Question

At a certain elementary school, 10 percent of the fifth-grade students are members of the school band. if 12 percent of the fifth-grade boys and 8 percent of the fifth-grade girls are members of the band, what percent of the fifth-grade students at the school are boys?

Answer 1

Let the 5-grade students be A in total.

Let b of these be boys, and g of these be girls, so b+g=A.

i) "At a certain elementary school, 10 percent of the fifth-grade students are members of the school band."

this means that the number of the members of the school band is :

$\frac{10}{100}A=0.1A=0.1(b+g)=0.1b+0.1g$

ii)
"12 percent of the fifth-grade boys and 8 percent of the fifth-grade girls are members of the band"

this means that the number of the band members is:
$\frac{12}{100}b+ \frac{8}{100}g=0.12b+0.08g$

equalizing these 2 ways of expressing the number of members of the band, we have:

$0.1b+0.1g=0.12b+0.08g$

$0.1g-0.08g=0.12b-0.1b$

$0.02g=0.02b$

so g=b

this means that 50% of the 5-grade students are boys.


Answer: 50%