Question

Suppose yogurt is on sale for $0.75 each, and you have a coupon for $0.50 off your total purchase. Write a function rule for the cost of x yogurts.
Number of yogurts: 1, 2, 3, 5, 7, x

Total cost: _ , _, _ ,_

Answer 1

Let's break down the cost of purchasing \( x \) yogurts.

1. **Cost of Yogurts**: Each yogurt costs $0.75, so the total cost for \( x \) yogurts without any coupon is given by:
\[
\text{Cost of } x \text{ yogurts} = 0.75x
\]

2. **Applying the Coupon**: You have a coupon for $0.50 off the total purchase. Therefore, the total cost after applying the coupon is:
\[
\text{Total cost with coupon} = 0.75x - 0.50
\]

Thus, the function rule for the cost of \( x \) yogurts, including the coupon discount, can be written as:
\[
C(x) = 0.75x - 0.50
\]

### Now, let's calculate the total costs for the specified values of \( x \):

- For \( x = 1 \):
\[
C(1) = 0.75(1) - 0.50 = 0.75 - 0.50 = 0.25
\]

- For \( x = 2 \):
\[
C(2) = 0.75(2) - 0.50 = 1.50 - 0.50 = 1.00
\]

- For \( x = 3 \):
\[
C(3) = 0.75(3) - 0.50 = 2.25 - 0.50 = 1.75
\]

- For \( x = 5 \):
\[
C(5) = 0.75(5) - 0.50 = 3.75 - 0.50 = 3.25
\]

- For \( x = 7 \):
\[
C(7) = 0.75(7) - 0.50 = 5.25 - 0.50 = 4.75
\]

### Total Costs:

- \( x = 1 \): $0.25
- \( x = 2 \): $1.00
- \( x = 3 \): $1.75
- \( x = 5 \): $3.25
- \( x = 7 \): $4.75

The total costs for the specified values of \( x \) are:
- For 1 yogurt: $0.25
- For 2 yogurts: $1.00
- For 3 yogurts: $1.75
- For 5 yogurts: $3.25
- For 7 yogurts: $4.75