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Write a system of equations to describe the situation below, solve using substitution, and fill in the blanks. The Hillsboro Tigers are having team shirts made. One option is to pay Clarence's Tees a $50 setup fee and then buy the shirts for $5 each. Another option is to go to City Printing, paying $36 for a setup fee and an additional $12 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 $◻.

Write a system of equations to describe the situation below, solve using substitution, and fill in the blanks.\newlineThe Hillsboro Tigers are having team shirts made. One option is to pay Clarence's Tees a $50 \$ 50 setup fee and then buy the shirts for $5 \$ 5 each. Another option is to go to City Printing, paying $36 \$ 36 for a setup fee and an additional $12 \$ 12 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?\newlineIf the Tigers have □\square shirts made, the cost is $□ \$ \square .

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Q. Write a system of equations to describe the situation below, solve using substitution, and fill in the blanks.\newlineThe Hillsboro Tigers are having team shirts made. One option is to pay Clarence's Tees a $50 \$ 50 setup fee and then buy the shirts for $5 \$ 5 each. Another option is to go to City Printing, paying $36 \$ 36 for a setup fee and an additional $12 \$ 12 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?\newlineIf the Tigers have □\square shirts made, the cost is $□ \$ \square .
  1. Define Variables and Equations: Define the variables and write the system of equations.\newlineLet xx represent the number of shirts and yy represent the total cost.\newlineFor Clarence's Tees:\newlineSetup fee: $50\$50\newlineCost per shirt: $5\$5\newlineEquation: Total cost yy = setup fee + (cost per shirt * number of shirts)\newliney=5x+50y = 5x + 50\newlineFor City Printing:\newlineSetup fee: $36\$36\newlineCost per shirt: $12\$12\newlineEquation: Total cost yy = setup fee + (cost per shirt * number of shirts)\newliney=12x+36y = 12x + 36\newlineSystem of equations:\newliney=5x+50y = 5x + 50\newliney=12x+36y = 12x + 36
  2. Substitution and Solving: Solve the system using substitution.\newlineSince both equations equal yy, set them equal to each other to find the number of shirts xx where the cost is the same.\newline5x+50=12x+365x + 50 = 12x + 36
  3. Isolate Variable x: Isolate the variable x.\newlineSubtract 5x5x from both sides of the equation:\newline5x+50−5x=12x+36−5x5x + 50 - 5x = 12x + 36 - 5x\newline50=7x+3650 = 7x + 36\newlineNow, subtract 3636 from both sides:\newline50−36=7x+36−3650 - 36 = 7x + 36 - 36\newline14=7x14 = 7x
  4. Solve for x: Solve for x.\newlineDivide both sides by 77 to find the value of xx:\newline147=7x7\frac{14}{7} = \frac{7x}{7}\newline2=x2 = x\newlineSo, x=2x = 2, which means the same cost occurs when 22 shirts are made.
  5. Find Total Cost: Find the total cost yy when x=2x = 2.\newlineSubstitute x=2x = 2 into one of the original equations to find yy. We'll use the equation from Clarence's Tees:\newliney=5(2)+50y = 5(2) + 50\newliney=10+50y = 10 + 50\newliney=60y = 60\newlineSo, the total cost yy is $60\$60 when 22 shirts are made.

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