Final answer:
To find when the costs from two companies are the same, set up an equation for each company and equate them. After solving the equation, it is determined that the cost will be the same for 20 shirts.
Step-by-step explanation:
To find out for what number of shirts the cost would be the same from the two companies, we need to set up an equation that equates the two cost functions.
Let x be the number of shirts the Hastings math club members are planning to order. The first company charges $9 per shirt plus a $65 setup fee. This gives us the equation 9x + 65 for the total cost from the first company.
The second company charges $7.50 per shirt plus a $95 fee. The equation for the total cost from the second company is 7.5x + 95.
To find when the costs are the same, we set the two equations equal to each other:
9x + 65 = 7.5x + 95
Solving for x by first rearranging terms and then isolating x:
- Subtract 7.5x from both sides: 1.5x + 65 = 95
- Subtract 65 from both sides: 1.5x = 30
- Divide by 1.5: x = 30 / 1.5
- x = 20
Therefore, the cost for both companies will be the same for 20 shirts.