Question

Meghan is buying some new shirts and sweaters. She is able to buy 6 shirts and 3 sweaters for $330 or she is able to buy 3 shirts and 2 sweaters for $204. How much does a sweater cost?

Answer 1

The cost of a sweater can be found by setting up a system of linear equations based on Meghan's purchases. After manipulating this system of equations, we find that a sweater costs $78.

Step-by-step explanation:

This problem is a system of linear equations problem. We can use the system of equations to determine the cost of a sweater and a shirt. Let's call the cost of a shirt 'S' and the cost of a sweater 'W'. The system of equations based on Meghan's purchases would be: 6S + 3W = $330 and 3S + 2W = $204.

By manipulating these equations, we can solve for 'S' and 'W'. By multiplying the second equation by two, our system becomes: 6S + 3W = $330 and 6S + 4W = $408. By subtracting the second equation from the first, we can solve for 'W': -W = -$78. Therefore, W = $78, meaning a sweater costs $78.

Learn more about Solving Linear Equations