Question: User: 8. T-Shirt Printing
Company A charges a $30 setup fee plus $8 per shirt. Company B charges a $60 setup fee plus $5 per shirt.
Write a system of equations to represent this relationship. Graph the equations and use the graph to determine the number of shirts that would cost the same from each company.
Be sure to use let statements to define variables!
1. **State the problem:**
We want to find the number of shirts where the total cost from Company A equals the total cost from Company B.
2. **Define variables:**
Let $x$ = number of shirts.
Let $y$ = total cost.
3. **Write the cost equations:**
Company A: $y = 30 + 8x$
Company B: $y = 60 + 5x$
4. **Set the equations equal to find when costs are the same:**
$$30 + 8x = 60 + 5x$$
5. **Solve for $x$:**
$$30 + 8x = 60 + 5x$$
$$8x - 5x = 60 - 30$$
$$3x = 30$$
$$x = \frac{30}{3}$$
$$x = 10$$
6. **Interpretation:**
At $x = 10$ shirts, both companies charge the same total cost.
7. **Find the total cost at $x=10$:**
$$y = 30 + 8(10) = 30 + 80 = 110$$
**Final answer:**
The cost is the same at 10 shirts, and the total cost is 110.