Question

The Hurricane print shop is having a super sale! All T-shirts, hoodies, and jackets are on sale and must go. Dylan purchased 6 T-shirts for $30. Zachery purchased 3 T-shirts and 2 hoodies for $37. Chris purchased 2 T-shirts, 4 hoodies, and 1 jacket for $69. Find the cost of each item.

a) Define your variables:
b) Write your equations:
c) Solve using substitution.

Answer 1

The cost of each item is found by defining variables T for T-shirts, H for hoodies, and J for jackets. By setting up a system of equations from the given purchases and solving using substitution, we find the prices to be $5 for T-shirts, $11 for hoodies, and $15 for jackets.

Step-by-step explanation:

Let's define the variables for the cost of each item:
Let T represent the cost of one T-shirt, H represent the cost of one hoodie, and J represents the cost of one jacket.

Based on the purchases we can write the following equations:
1. For Dylan's purchase of 6 T-shirts for $30: 6T = 30
2. For Zachery's purchase of 3 T-shirts and 2 hoodies for $37: 3T + 2H = 37
3. For Chris's purchase of 2 T-shirts, 4 hoodies, and 1 jacket for $69: 2T + 4H + J = 69

Solving Using Substitution

1. Solve the first equation for T: T = 30/6, T = 5.
2. Substitute T = 5 into the second equation: 3(5) + 2H = 37, 15 + 2H = 37, 2H = 22, H = 11.
3. Substitute T = 5 and H = 11 into the third equation: 2(5) + 4(11) + J = 69, 10 + 44 + J = 69, J = 69 - 54, J = 15.

So the cost of each item is $5 for a T-shirt, $11 for a hoodie, and $15 for a jacket.