Question

Write a system of equations to describe the situation below, solve using elimination, and fill in the blanks. A group of friends are at a baseball game and are purchasing souvenirs. Jessica purchased 3 t-shirts and 2 baseball caps, spending a total of $141. Her Raymond purchased 3 t-shirts and 1 baseball cap, which cost him a total of $111. Assuming that all of the t-shirts and all of the caps are the same price, what is the price of each?

Answer 1

To write a system of equations to describe the situation, assign variables to represent the price of a t-shirt and a baseball cap. Solve the system using elimination to find the prices. The price of each t-shirt is $40.50.

Step-by-step explanation:

To write a system of equations describing the situation, let's assign variables to represent the price of a t-shirt and the price of a baseball cap. Let 't' be the price of a t-shirt, and 'c' be the price of a baseball cap.

From the given information, we can write the following system of equations:

3t + 2c = 141 (Equation 1)

3t + c = 111 (Equation 2)

To solve this system of equations using elimination, we can subtract Equation 2 from Equation 1:

(3t + 2c) - (3t + c) = 141 - 111

t + c = 30

Now, we can solve the simplified equation:

We can substitute the value of c from the simplified equation into either of the original equations to find the value of t. Let's substitute it into Equation 2:

3t + (30 - t) = 111

2t + 30 = 111

2t = 111 - 30

2t = 81

t = 81/2

t = 40.50

Therefore, the price of each t-shirt is $40.50.