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Write a system of equations to describe the situation below, solve using substitution, and fill in the blanks.The Oakland Tigers are having team shirts made. One option is to pay Joey's Tees a setup fee and then buy the shirts for each. Another option is to go to City Printing, paying for a setup fee and an additional 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. How many shirts is that? What is the cost?If the Tigers have _____ shirts made, the cost is _____.
Full solution
Q. Write a system of equations to describe the situation below, solve using substitution, and fill in the blanks.The Oakland Tigers are having team shirts made. One option is to pay Joey's Tees a setup fee and then buy the shirts for each. Another option is to go to City Printing, paying for a setup fee and an additional 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. How many shirts is that? What is the cost?If the Tigers have _____ shirts made, the cost is _____.
- Define Variables: Let's define the variables.Let be the number of shirts.Let be the total cost.For Joey's Tees, the cost equation is:For City Printing, the cost equation is:
- Set Up Equations: Set up the system of equations.Joey's Tees: City Printing:
- Substitution to Solve: Use substitution to solve for .Since both equations equal , we can set them equal to each other:
- Solve for x: Solve for x.Subtract from both sides:Subtract from both sides:
- Solve for y: Use the value of to solve for .We can use either of the original equations. Let's use Joey's Tees equation:
- Check Solution: Check the solution with the City Printing equation.Since the cost is the same for both equations, our solution is correct.
