Final answer:
To calculate the total cost after a 15% discount on the installation price, subtract 15% of $500 from the installation cost and add it to the cost of the carpet. The expression is $2375 + ($500 - ($500 * 0.15)), which simplifies to $2800, covering both the discounted installation and carpet cost.
Step-by-step explanation:
The expression needed to find the total cost Sonja will pay for the installation and new carpet after using the coupon is calculated by applying the discount to the installation price and adding this to the cost of the carpet.
The installation price is $500, and Sonja has a 15% off coupon.
To calculate the discounted installation price, multiply $500 by the discount rate of 15% (0.15), which gives us the discount amount of $75.
Subtract the discount from the installation price to get the reduced installation cost: $500 - $75 = $425.
Now, add this to the cost of the carpet, which is $2875 - $500 (installation price) = $2375.
The total cost is therefore $2375 (carpet) + $425 (discounted installation) = $2800.
To express this algebraically: Total Cost = Carpet Cost + (Installation Cost - (Installation Cost * Discount Rate))
Total Cost = $2375 + ($500 - ($500 * 0.15))
Simplifying the expression: Total Cost = $2375 + ($500 - $75)
Finally, Total Cost = $2375 + $425
= $2800