Marisol orders custom T-shirts for her club. The supplier charges a setup fee of $48 plus $7.25 for each T-shirt. A coupon code gives her a 12% discount on the entire order, including the setup fee. If Marisol’s final cost after applying the discount is $638, which equation represents the number of T-shirts, , she ordered?
A one-time fee plus a price per item gives the cost before a coupon. A discount multiplier tells you what fraction of that cost remains after a percent is taken off. If the discount covers the entire order, multiply the whole sum, then set it equal to the final charge. Subtracting a percent as a flat dollar amount mixes two different kinds of quantities.
Hints
- Hint 1
A setup fee is charged once, while a per-shirt price is multiplied by the number of shirts. What expression adds those two charges before the coupon is applied?
- Hint 2
A discount takes away part of the original cost. Start with the whole cost as , then subtract the decimal form of the percent taken off. What fraction is left to pay?
- Hint 3
An equation says two amounts are equal. The discounted total, not the price before the coupon, must equal Marisol’s final cost.
Step-by-step
Build the cost, then apply the discount
Step 1Build the price before the coupon
No Desmos needed. You’re choosing an equation, not solving for .
The shirts cost dollars at $7.25 each. The $48 setup fee is charged once, so add it to the shirt cost:
- Step 2
Find the share Marisol pays
A discount multiplier is the fraction of the original cost left to pay. The whole cost is times itself, and is taken off. Subtract that share:
Using alone would give the amount discounted, not the final cost.
- Step 3
Apply the discount to the whole order
The coupon covers the entire order, including the setup fee, so multiply the whole pre-discount sum by the share Marisol pays:
Apply a percent to its whole base, not to only one part of that base.
- Step 4
Match the final cost
The $638 is the cost after the coupon, so set the discounted total equal to it:
This equation represents the number of T-shirts Marisol ordered. Choice D.