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.