x - the cost of the skirt
y - the cost of the blouse
The ratio of the cost of the skirt to the cost of the blouse is 8:5.
[tex]\frac{x}{y}=\frac{8}{5} \\ 5x=8y \\ x=\frac{8}{5}y[/tex]
The skirt costs $24 more than the blouse.
[tex]x=y+24[/tex]
Set (8/5)y and y+24 equal to each other:
[tex]\frac{8}{5}y=y+24 \\
\frac{8}{5}y-y=24 \\
\frac{8}{5}y-\frac{5}{5}y=24 \\
\frac{3}{5}y=24 \\
y=24 \times \frac{5}{3} \\
y=8 \times 5 \\
y=40[/tex]
The cost of the blouse is $40.
