Question 482·Easy·Algebra

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$C = 45 + 3n$

In the equation above, $C$ represents the total cost, in dollars, to print $n$ custom T-shirts at a shop, where $45$ is a one-time setup fee and $3$ is the cost per T-shirt. If the total cost was $120, how many T-shirts were printed?

A linear cost model adds a one-time fee to a per-item charge. Given the total, substitute it for the cost and use a Desmos regression to find the item count. Only the money left after the one-time fee pays for items. Dividing the full total by the item price wrongly counts the fee as item spending.

Hints

Hint 1
The setup fee is paid once, no matter how many shirts are printed. In the cost equation, which term changes with the number of shirts? Keep the fee separate when you replace $C$ with the given total.
Hint 2
A regression lets Desmos find an unknown in an equation. After replacing $C$ with the total, type the equation with $\sim$ in place of $=$ . What value does Desmos report for $n$ ?

Step-by-step

Substitute the total and solve
Step 1
Write the equation for the given total
Since $C$ means total cost and the total was $120, replace $C$ with $120$ in the given equation: $120=45+3n$ . The setup fee is paid once. Only the $3 per shirt is multiplied by $n$ .
Step 2
Find the number of shirts
Type $120\sim45+3n$ in Desmos. The $\sim$ makes this a regression: Desmos finds $n$ instead of making it a slider. Under PARAMETERS, it reports $n=25$ . Since $n$ counts shirts, 25 T-shirts were printed. Choice D.

Question 482·Easy·Algebra

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