Two sales totals involving the same two prices signal a system of equations: each day gives one equation. Name the original shirt price and the mug price, then apply the discount only to Tuesday’s shirts. Graph both equations in Desmos and click their intersection to read the mug price. Using the original shirt price on Tuesday ignores the discount.
Hints
- Hint 1
For a sales total, multiply each item’s price by its quantity before adding. Give the original shirt price and the unchanged mug price separate letters. How would you write Monday’s total?
- Hint 2
A discount of leaves of the original price. Use that smaller price for Tuesday’s shirts, but keep the mug price the same.
- Hint 3
A system is two equations that must both be true. Their intersection in Desmos gives both prices. Which coordinate represents the mug price you named?
Step-by-step
Model both days and graph the system
Step 1Write Monday’s total
Let be one T-shirt’s original price and be one mug’s price. Monday’s money from each item adds to the given total, so:
- Step 2
Find Tuesday’s shirt price
A discount of means you keep of the original price:
So each Tuesday shirt costs . The mug price does not change.
- Step 3
Write Tuesday’s total
Tuesday’s three shirts cost altogether, while five mugs cost . Add those amounts to match the Tuesday total:
Putting on the mug term instead would discount the wrong item.
- Step 4
Read the mug price at the intersection
Type both equations in Desmos on separate lines. Click their intersection, the point that makes both totals true. Desmos shows . The second coordinate is , so one mug cost $15. Choice C.