A person purchases

Question

2 tricycles using a coupon and a store discount. The coupon is applied first and takes a certain number of dollars off the purchase before the store discount is applied to the total purchase.

If the expression 0.75 (2x - 5)
represents the final cost, in dollars, where
is the original price of each tricycle, in dollars, what does the value 0.75
represent?

Responses

The value of the coupon is $ 75 off.

The value of the coupon is $25 off.

The store discount on the total purchase is 75%
off.

The store discount on the total purchase is 75 % % off.

The store discount on the total purchase is 25%
off.

Answer 1

To analyze the expression \( 0.75(2x - 5) \), let's break it down.

1. Understanding the context: The person purchases 2 tricycles with a coupon and a store discount. The original price of each tricycle is \( x \), so the total price before any discounts is \( 2x \). The coupon applies first and takes off a certain dollar amount (which we see as the \( -5 \) in \( 2x - 5 \)). After the coupon is applied, the total is then multiplied by 0.75.

2. Interpreting the multiplication by 0.75: The factor of 0.75 suggests that the total amount after the coupon is further reduced. Specifically, multiplying by 0.75 means that the customer is paying 75% of the price after the coupon has been applied. This indicates a 25% store discount on the amount after the coupon is applied since \( 1 - 0.75 = 0.25\).

Therefore, we conclude that:

• The value of the coupon is represented by the \( -5 \) (not given in the options).
• The \(0.75\) represents that the store discount on the total purchase is 25% off, because after applying the coupon, the remaining amount is reduced to 75% of its value.

The correct answer is:

The store discount on the total purchase is 25% off.