Question 60·Hard·Linear Equations in One Variable
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?
For word problems that ask for an equation, first translate each part of the story into algebra: write the original total (fixed fee plus per-item cost times quantity), then handle discounts or taxes as multipliers on that total (e.g., a 12% discount means multiply by ). Finally, set this expression equal to the given final amount and choose the answer whose structure matches your expression rather than trying to solve for the variable unless the question specifically asks for its value.
Hints
Identify the original total cost
Before any discount, how would you write the total cost combining the fixed setup fee and the per-shirt cost for shirts?
Think about what a 12% discount does
If you take 12% off a price, what percent of the original price do you actually pay? How can you write that as a decimal or as ?
Apply the discount to the right quantity
Does the 12% discount apply only to the shirts, only to the setup fee, or to the entire original total cost you wrote in the first hint?
Connect to the final cost
Once you have an expression for the discounted total cost, how do you use the fact that Marisol actually paid $638?
Desmos Guide
Write the original total cost
In a Desmos line, type 48 + 7.25n to represent the total cost before any discount (setup fee plus shirts).
Model the discount in Desmos
In a new line, multiply that expression by the fraction of the price Marisol actually pays after a 12% discount, for example by a decimal less than 1 (like 0.88) or by (1 - 0.12). This represents the discounted total cost.
Connect to the final cost and compare to choices
Now imagine setting this discounted expression equal to 638 (her final cost). Look back at the answer choices and see which equation has the same structure: the entire original total being multiplied by the discount factor and set equal to 638.
Step-by-step Explanation
Write an expression for the original (pre-discount) cost
The supplier charges a setup fee plus a cost per shirt.
- Setup fee:
- Cost per shirt: for each of shirts, or
So the total cost before any discount is:
Model the 12% discount as a multiplier
A 12% discount means you pay 100% − 12% = 88% of the original price.
- As a decimal, 88% is .
- Another way to write 88% of a number is times that number.
So the final cost after discount is:
Set the discounted cost equal to the final price and match the equation
We are told Marisol’s final cost is $638, so we set the discounted expression equal to $638:
This matches answer choice D.