Let x be the pre-sale price of the sweater at Sweater village and y be the pre-sale price of the sweater at Winter Wonderland.
Discount at Sweater Village = 20%
[tex]=\frac{20}{100} x[/tex]
[tex]=\frac{x}{5}[/tex]
Cost after discount = [tex]x-\frac{x}{5} =\frac{4x}{5}[/tex]
[tex]\frac{4x}{5}=45[/tex]
[tex]x=\frac{5(45)}{4}[/tex]
=[tex]\frac{225}{4}[/tex]
x = 56.25
Discount at Winter Wonderland = 25%
[tex]=\frac{25}{100} y[/tex]
[tex]=\frac{y}{4}[/tex]
Cost after discount = [tex]y-\frac{y}{4}[/tex]
=[tex]\frac{3y}{4}[/tex]
[tex]\frac{3y}{4}[/tex]=42
y = 56
Difference in cost = 56.25 - 56 = 0.25
Hence, sweater at Sweater Village costs 0.25 more than at Winter Wonderland.
