Question

The Vindale Tigers are having team shirts made. One option is to pay Anita's Tees a $25 setup fee and then buy the shirts for $5 each. Another option is to go to City Printing, paying $30 for a setup fee and an additional $4 per shirt. The team parent in charge of the project notices that, with a certain number of shirts, the two options have the same cost. What is the cost? Write a system of equations, graph them, and type the solution.

Answer 1

`\begin{gathered} 5\text{ shirts} \\ \text{total cost: \$ 50} \end{gathered}`

Step-by-step explanation

Step 1

Let x represents the number of shirts

then

Option 1

One option is to pay Anita's Tees a $25 setup fee and then buy the shirts for $5 each

`Cost_1=25+5x`

and, Another option is to go to City Printing, paying $30 for a setup fee and an additional $4 per shirt

`\text{Cost}_2=30+4x`

now, there is a value for x, that makes cost1=cost 2, Hence

`25+5x=30+4x\text{ Equation(1)}`

Step 2

solve the equation

`\begin{gathered} 25+5x=30+4x\text{ Equation(1)} \\ subtract\text{ 4x in both sides} \\ 25+5x-4x=30+4x-4x \\ 25+x=30 \\ \text{subtract 25 in both sides} \\ 25+x-25=30-25 \\ x=5 \end{gathered}`

so, the number of shirts is 5

Step 3

finally, replace the value of x = 5, to know the cost

`\begin{gathered} Cost_1=25+5x \\ Cost_1=25+5\cdot5 \\ Cost_1=25+25 \\ Cost_1=Cost_2=50 \end{gathered}`

Step 4

graph

green line-equation (1)

red line= equation (2)

I hope this helps you