Question

During a clothing store's Bargain Days, the regular price for t-shirts is discounted to $4.50 each. You have an additional coupon for $3.00 off the total purchase, regardless of how many shirts are purchased. Write a rule for the function `p(x)` that expresses the final sale price of `x` t-shirts with the coupon applied.

Number of T-shirts: 1,2,3, t
Total cost:

Answer 1

To determine the final sale price \( p(x) \) of \( x \) t-shirts with the discount applied, we can follow these steps:

1. **Determine the regular total price before the coupon**: Each t-shirt costs $4.50, so for \( x \) t-shirts, the total price will be:
\[
\text{Total price} = 4.50 \times x
\]

2. **Apply the coupon**: You have an additional discount of $3.00 on the total purchase. Therefore, the total cost after applying the coupon will be:
\[
\text{Final price} = (4.50 \times x) - 3.00
\]

Putting it all together, the rule for the function \( p(x) \) that expresses the final sale price for \( x \) t-shirts is:
\[
p(x) = 4.50x - 3.00
\]

Where \( x \) is the number of t-shirts purchased.

Thus, for specific numbers of t-shirts:

- If \( x = 1 \):
\[
p(1) = 4.50 \times 1 - 3.00 = 1.50
\]

- If \( x = 2 \):
\[
p(2) = 4.50 \times 2 - 3.00 = 6.00 - 3.00 = 3.00
\]

- If \( x = 3 \):
\[
p(3) = 4.50 \times 3 - 3.00 = 13.50 - 3.00 = 10.50
\]

- If \( x = t \) (where \( t \) is any number of t-shirts):
\[
p(t) = 4.50t - 3.00
\]

This function \( p(x) \) gives the final price for any number of t-shirts bought during the sale.