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=

Answer 1

To express the final sale price of \( x \) t-shirts using the function \( p(x) \), we need to take into account both the discounted price of the t-shirts and the additional coupon. Here's how to formulate it:

1. The regular discounted price for one t-shirt is $4.50.
2. The total cost for \( x \) t-shirts before applying the coupon is \( 4.50x \).
3. The additional coupon provides a $3.00 discount on the total purchase.

The final sale price \( p(x) \) can be expressed as follows:

\[
p(x) = 4.50x - 3.00
\]

Now, we can calculate the final sale price for a few scenarios:

- For 1 t-shirt \((x=1)\):
\[
p(1) = 4.50(1) - 3.00 = 4.50 - 3.00 = 1.50
\]

- For 2 t-shirts \((x=2)\):
\[
p(2) = 4.50(2) - 3.00 = 9.00 - 3.00 = 6.00
\]

- For 3 t-shirts \((x=3)\):
\[
p(3) = 4.50(3) - 3.00 = 13.50 - 3.00 = 10.50
\]

- For \( t \) t-shirts:
\[
p(t) = 4.50t - 3.00
\]

So, the rule for the function \( p(x) \) that expresses the final sale price of \( x \) t-shirts with the coupon applied is:

\[
p(x) = 4.50x - 3.00
\]