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 or Yogurts:
1=
2=
3=
5=
7=
x=

Answer 1

To create a function rule for the cost of \( x \) yogurts, we start by calculating the cost before applying the coupon.

The cost of \( x \) yogurts at $0.75 each can be represented as:

\[
\text{Cost} = 0.75x
\]

Then, we subtract the coupon value of $0.50 from the total cost:

\[
\text{Total Cost} = 0.75x - 0.50
\]

Therefore, the function rule for the total cost \( C(x) \) of \( x \) yogurts is:

\[
C(x) = 0.75x - 0.50
\]

Now, we can calculate the cost for different quantities of yogurt:

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

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

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

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

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

6. For \( x \):
\[
C(x) = 0.75x - 0.50
\]

Here is the summarized calculation for the number of yogurts:

- **Number of Yogurts**:
- 1 = $0.25
- 2 = $1.00
- 3 = $1.75
- 5 = $3.25
- 7 = $4.75
- \( x = 0.75x - 0.50 \) (for any \( x \))