Two unknown original prices and two separate totals cue a system of equations: write one equation for each fact, then compare the choices. You don't need to solve for either price. For the final-payment equation, multiply each original price by the percent still paid, then subtract the fixed coupon once. The discount percentages measure savings, not payment.
Hints
- Hint 1
A system is two equations that must both be true. The original-price total is one fact, separate from the final amount paid. Which two original-price letters must add to the total before any discounts?
- Hint 2
A discount tells you the part removed, not the part charged. For the amount paid, subtract each discount percent from and multiply the original price by the percent left.
- Hint 3
The coupon comes off once, after the discounted jersey prices are added. It isn't applied separately to each jersey. What expression represents the combined price after that subtraction?
Step-by-step
Write an equation for each total
Step 1Write the original-price total
No Desmos needed. You're building the system, not solving it. The jerseys' original prices total $160, so
This equation counts dollars before either discount.
- Step 2
Find the prices after each discount
A discount removes a percent of the original price. The home jersey keeps , so its discounted price is . The away jersey keeps , so its discounted price is . Multiply by the percent kept, not the percent removed.
- Step 3
Take off the coupon once
The coupon takes another $10 off the combined discounted price, so add the two prices and then subtract $10:
- Step 4
Match the final payment
The amount paid is $107, so the expression after the coupon must equal 107:
Together with , this forms the system, the two equations the original prices must satisfy. Choice D.