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The ratio of the skirt to the cost of a blouse is 8:5. If the skirt costs $24 more than the blouse, find the cost of the blouse.

Sagot :

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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.
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