Question 97·Easy·Linear Functions
In the equation above, represents the total cost, in dollars, to print custom T-shirts at a shop, where is a one-time setup fee and is the cost per T-shirt. If the total cost was $120, how many T-shirts were printed?
For linear cost problems, translate the situation into an equation by plugging the given total cost into the cost formula, then solve step by step using inverse operations: subtract the fixed fee first, then divide by the per‑item cost. Always check your answer quickly by substituting it back into the original equation to confirm the total matches the problem.
Hints
Use the given equation
You are told the total cost was $120. In the equation , what should you substitute for ?
Set up the equation to solve for n
After substituting the total cost, you will get an equation of the form . How can you start isolating on one side?
Finish solving the equation
Once you have by itself, what operation undoes multiplying by 3 so you can find ?
Desmos Guide
Enter the cost function
In Desmos, type y = 45 + 3x to represent the total cost as a function of the number of T‑shirts .
Enter the total cost line
On the next line, type y = 120 to represent the given total cost.
Find the number of T-shirts
Look for the intersection point of the two graphs. The x-coordinate of this intersection is the number of T‑shirts printed that gives a total cost of $120.
Step-by-step Explanation
Write the equation for this specific situation
You are told the total cost was $120, and the cost model is .
Substitute into the equation:
Now you have an equation with just one variable, , to solve.
Isolate the term with n
To get by itself, first remove the constant term on the right.
Subtract 45 from both sides:
So:
Now is only being multiplied by 3.
Solve for n
To solve , divide both sides by 3:
So . This means 25 T‑shirts were printed.