[tex]\huge\boxed{\text{$74$ girls}}\ \huge\boxed{\text{$106$ boys}}[/tex]
Hey there! This situation can be modeled and solved using a system of equations. We'll use [tex]b[/tex] to represent the number of boys and [tex]g[/tex] to represent the number of girls.
[tex]\displaystyle{\left \{ {{b+g&=180} \atop {b&=g+32} \right.}[/tex]
Since we know what [tex]b[/tex] equals, we can substitute it into the first equation.
[tex]\begin{aligned}b+g&=180\\(g+32)+g&=180&&\smash{\Big|}&&\text{Substitute.}\\2g+32&=180&&\smash{\Big|}&&\text{Combine like terms.}\\2g&=148&&\smash{\Big|}&&\text{Subtract $32$ from both sides.}\\g&=74&&\smash{\Big|}&&\text{Divide both sides by $2$.}\end{aligned}[/tex]
Now that we know the number of girls, use the second equation to get the number of boys.
[tex]\begin{aligned}b&=g+32\\&=74+32&&\smash{\Big|}&&\text{Substitute.}\\&=106&&\smash{\Big|}&&\text{Add.}\end{aligned}[/tex]
