Question

I was able to buy 6 shirts and 1 sweater for $334 or 3 shirts and 4 sweaters for 664. how much does a shirt and sweater cost

Answer 1

Using systems of equations, we calculate the price of a shirt to be $32 and the price of a sweater to be $142.

Step-by-step explanation:

The student is asking how much a shirt and a sweater cost individually based on two different combined purchases. This problem is an example of a system of linear equations, which can be solved using algebra.

We can set up the following system of equations based on the purchases:

• 6S + W = $334 (1)
• 3S + 4W = $664 (2)

To solve the system, we can use the substitution or elimination method. For instance, we can multiply equation (1) by 4 to eliminate the W variable:

• 24S + 4W = $1336 (3)

Then, subtract equation (2) from equation (3):

• 24S + 4W - (3S + 4W) = $1336 - $664
• 21S = $672
• S = $32

Now that we have the price of one shirt (S), we can substitute it back into equation (1) to find the price of one sweater (W).

6($32) + W = $334

• $192 + W = $334
• W = $334 - $192
• W = $142

The price of a shirt is $32 and the price of a sweater is $142.