Question

A store is having a big sale. The cost of 3 hats, 6 shirts, and 2 pairs of shorts is $108. The cost of 2 hats, and 8 pairs of shorts is $112. The cost of 5 shirts and 3 pairs of shorts is $86. Find how much each hat, shirt, and pair of shorts cost."

Answer 1

The problem is solved by setting up a system of linear equations with three variables representing the cost of a hat, shirt, and pair of shorts, and solving them simultaneously using methods like substitution, elimination or matrix operations.

Step-by-step explanation:

To find the cost of each hat, shirt, and pair of shorts individually, we need to set up a system of equations based on the information provided. Let's define the variables as follows: H for the cost of one hat, S for the cost of one shirt, and P for the cost of one pair of shorts.

The system of equations based on the store's sale is:

1. 3H + 6S + 2P = $108
2. 2H + 0S + 8P = $112
3. 0H + 5S + 3P = $86

By solving these equations simultaneously, we will determine the individual prices of a hat, a shirt, and a pair of shorts. We can use methods such as substitution, elimination, or matrix operations to solve the system. This is a good example of applying linear algebra to solve real-world problems.