Question

A t-shirt printing company will charge $25 design fee plus $8 per t-shirt. Another company will charge $35

design fee plus $6 per shirt for the same design. For how many shirts will the costs be the same (equal) regardless of which company is used?

Answer 1

To find out when the costs from two t-shirt companies will be the same, we solve the equation 25 + 8x = 35 + 6x where x represents the number of t-shirts. After simplifying, we discover that the costs are the same when 5 shirts are purchased.

Step-by-step explanation:

1. The student's question asks when the cost of t-shirts from two different companies will be the same given their individual pricing structures. One company charges a $25 design fee plus $8 per t-shirt, while the other charges a $35 design fee plus $6 per shirt. To find out for how many shirts the costs will be the same, we need to set up an equation where the total cost from both companies is equal and solve for the number of shirts.

1. Step-by-Step Solution:

1. Let's denote the number of t-shirts as x.

1. For the first company, the total cost is $25 (design fee) + $8x (cost per t-shirt).

1. For the second company, the total cost is $35 (design fee) + $6x (cost per t-shirt).

1. We set up the equation 25 + 8x = 35 + 6x.

1. To find the value of x, we solve the equation:

1. Subtract 6x from both sides to get 2x = 10.

1. Divide both sides by 2 to get x = 5.

1. Therefore, the costs will be equal for 5 t-shirts.