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Mrs. Owens has a coupon for 40% off a pair of shoes. She pays $111.79 for a pair of shoes and a dress after using the coupon. The dress costs $64.99. Which equation can be solved for x, the retail price of the shoes?

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Final answer:

To find the retail price of the shoes before the coupon discount, use the equation 0.60x + $64.99 = $111.79 and solve for x. Subtract the price of the dress and divide by 0.60 to get the original price of the shoes, which is $78.00.

Step-by-step explanation:

Mrs. Owens has a coupon for 40% off a pair of shoes, and the total cost she pays for the shoes and a dress is $111.79. If the dress costs $64.99, we need to find the retail price of the shoes, which we'll call x. With the coupon, Mrs. Owens would pay 60% of the retail price for the shoes, because a 40% discount means she pays 100% - 40% = 60% of the original price.

To set up the equation, we will represent the 60% as 0.60, and put everything together. The retail price of the shoes minus 40% of it, plus the price of the dress, equals the total amount paid: 0.60x + $64.99 = $111.79

Now, to solve for x, the retail price of the shoes, we first subtract the price of the dress from both sides of the equation:

0.60x = $111.79 - $64.99

0.60x = $46.80

Then we divide both sides by 0.60 to find x:

x = $46.80 / 0.60

x = $78.00

So, the retail price of the shoes before the discount was applied is $78.00.

User Amal Murali
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