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 :


`(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:

`(12)/(100)b+ (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%