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 :
[tex] \frac{10}{100}A=0.1A=0.1(b+g)=0.1b+0.1g [/tex]
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:
[tex] \frac{12}{100}b+ \frac{8}{100}g=0.12b+0.08g[/tex]
equalizing these 2 ways of expressing the number of members of the band, we have:
[tex]0.1b+0.1g=0.12b+0.08g[/tex]
[tex]0.1g-0.08g=0.12b-0.1b[/tex]
[tex]0.02g=0.02b[/tex]
so g=b
this means that 50% of the 5-grade students are boys.
Answer: 50%
