Question

softball club wants to order shirts with their club logo. one company charges \\$8 per shirt plus an initial setup fee of \\$110. another company charges \\$12 per shirt plus an initial setup fee of \\$50. for what number of shirts would the cost be the same?

what is the solution to this system of equations?

Explanation:

Formulate the equations

We define variables:
\(x\): number of shirts
\(y\): total cost

Using Algebraic Word Problems:
First company:

$$y = 8x + 110$$

Second company:

$$y = 12x + 50$$

Solve for equal cost

Using System of Linear Equations:
Set the costs equal:

$$12x + 50 = 8x + 110$$

$$4x = 60$$

$$x = 15$$

Find the cost value

Substitute \(x = 15\) back:

$$y = 8(15) + 110 = 230$$

The cost is the same for 15 shirts.

Identify the graphical solution

The intersection point is:

$$(x, y) = (2, 1)$$

This is the solution to the system shown on the grid.

Answer:

Question 1

15 shirts

Question 2

\((2, 1)\)