Question 383·Medium·Algebra

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A local charity sold T-shirts and coffee mugs to raise funds, earning a total of $2,316. The relationship is modeled by the equation $18t + 12m = 2,316$ , where $t$ is the number of T-shirts sold and $m$ is the number of coffee mugs sold. If the charity sold $70$ coffee mugs, how many T-shirts did it sell?

Your answer

A two-variable linear equation can describe how two kinds of sales add up to one total. When the count for one kind is given, substitute it into the matching term and solve for the other count. A Desmos regression can handle the remaining equation. Keep dollars separate from items: you must subtract the money earned from mugs, not the number of mugs.

Hints

Hint 1
The coefficient $12$ is the price of one mug, so $12m$ is the money earned from all the mugs. Put the known mug count in place of $m$ . What letter is still unknown?
Hint 2
After substituting, use a regression in Desmos to find the value that makes both sides equal. Replace the unknown T-shirt count with $x_1$ so Desmos solves for it.

Step-by-step

Substitute the mug count and solve
Step 1
Put the known count in the right term
The problem says $m$ counts mugs, so the $70$ mugs belong in $12m$ , not $18t$ . Each term is money earned from that item. Substitute $m=70$ :
$18t+12(70)=2,316$
Step 2
Find the T-shirt count
Type $18x_1+12(70)\sim2316$ in Desmos. Here $x_1$ stands for $t$ , and $\sim$ tells Desmos to find the value that balances the equation. Under PARAMETERS, it shows $x_1=82$ . So the charity sold $82$ T-shirts. Grid in 82.

Question 383·Medium·Algebra

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