Question

There is a 25 cent discount per apple if 4 are purchased. Eve was making apple pie this weekend and bought 12 apples for $15. To find the original price of each apple, which represents the equation to solve the problem algebraically?
Responses

3(x−0.25)=15

12(x−0.25)=15

12(x+0.25)=15

3(x+0.25)=15

Answer 1

To determine the original price of each apple (denoted as \( x \)), we also need to factor in the discount given when 4 apples are purchased. If the discount is 25 cents per apple when 4 are purchased, it implies that for the 12 apples Eve bought, she received a total discount, but only on the quantity that is a multiple of 4 (which is 8 apples, resulting in 2 full discounts).

1. **Calculate the total discount**: Since she bought 12 apples, and assuming the discount applies to every group of 4 apples, for 12 apples, she receives a discount on 8 apples (because \( 12 \div 4 = 3 \), which means 3 groups), hence:
- Total discount for 12 apples = \( 3 \times 0.25 = 0.75 \).

2. **Calculate the effective payment for 12 apples**: She paid $15 after getting the discount for 12 apples. Therefore, if we let \( x \) be the original price of each apple, the equation accounting for the discount on the effective price for the apples she bought is:
- The effective price (after discount) is \( x - 0.25 \).
- Total cost of the apples can be computed as \( 12(x - 0.25) \).

Thus, the equation to represent the situation is:
\[
12(x - 0.25) = 15
\]

To answer your question, the correct response is:
**12(x − 0.25) = 15**.