Answer:
There are 40 girls and 24 boys in the camp
Step-by-step explanation:
let [tex]b[/tex] be the number of boys and [tex]g[/tex] be the number of girls in the camp, then when know that
[tex]\dfrac{b}{g} = \dfrac{3}{5}[/tex] (this says that the ratio of boys to girls is 3: 5)
And since there are a total of 64 campers, we have
[tex]b+g =64[/tex] (this says that the total number of boys an girls must 64)
Thus, we have two equations and two unknowns:
[tex](1). \: \: \dfrac{b}{g} = \dfrac{3}{5}[/tex]
[tex](2). \: \:b+g =64[/tex]
and we solve this system by first solving for [tex]b[/tex] in equation (1):
[tex]b= \dfrac{3}{5}g,[/tex]
and substituting it into equation (2):
[tex]\dfrac{3}{5}g+g=64[/tex]
solving for [tex]g[/tex] we get:
[tex]\boxed{g=40}[/tex].
Putting [tex]g=40[/tex] into equation (2), we solve for [tex]b[/tex] to get:
[tex]b+40=64[/tex]
[tex]\boxed{b=24}[/tex]
Thus, there are 40 girls and 24 boys in the camp.
