As president of the student council, Meg is choosing between two options for class T-shirts. A local shop charges $11 for each shirt, plus a set-up fee of $100. An online store charges $15 for each shirt, plus a set-up fee of $24. Which equation can you use to find s, the number of shirts Meg would need to order for the two options to cost the same? Choices: (A)11 + 100s = 15 + 24s (B)11s + 100 = 15s + 24 How many shirts would Meg need to order for the two options to cost the same? ____ shirts

Question

As president of the student council, Meg is choosing between two options for class T-shirts. A local shop charges $11 for each shirt, plus a set-up fee of $100. An online store charges $15 for each shirt, plus a set-up fee of $24. Which equation can you use to find s, the number of shirts Meg would need to order for the two options to cost the same?   Choices: (A)11 + 100s = 15 + 24s (B)11s + 100 = 15s + 24  How many shirts would Meg need to order for the two options to cost the same?   ____ shirts

Bytelearn · Accepted Answer

Set Up Equations: Let's set up the equations for the total cost of the shirts for each option. For the local shop, the total cost C is the number of shirts s times the price per shirt plus the set-up fee: C = 11s + 100. For the online store, the total cost C is also the number of shirts s times the price per shirt plus the set-up fee: C = 15s + 24. To find the number of shirts s that makes the costs equal, we set the two expressions for C equal to each other.Write Equation: Now we write the equation that equates the two costs: 11s + 100 = 15s + 24. This is the equation we can use to solve for s, the number of shirts needed for the costs to be the same.Solve for s: To solve for s, we need to get all the terms with s on one side and the constants on the other side. We can do this by subtracting 11s from both sides of the equation: 11s + 100 - 11s = 15s + 24 - 11s.Isolate Term: Simplifying both sides of the equation gives us: 100 = 4s + 24.Subtract Constants: Next, we subtract 24 from both sides to isolate the term with s: 100 - 24 = 4s + 24 - 24.Divide by 4: This simplifies to 76 = 4s.Finally, we divide both sides by 4 to solve for s: 76 / 4 = 4s / 4.This gives us s = 19. So, Meg would need to order 19 shirts for the two options to cost the same.

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