Michael spent $131 on shirts. Polo shirts cost $28, and T-shirts cost $15. If he bought a total of 7 shirts, then how many of each kind did he buy? Solve algebraically.(1 point)

Question

Responses

3 Polos and 4 T-shirts
3 Polos and 4 T-shirts

5 Polos and 2 T-shirts
5 Polos and 2 T-shirts

2 Polos and 5 T-shirts
2 Polos and 5 T-shirts

4 Polos and 3 T-shirts

Answer 1

Let \( p \) be the number of polo shirts and \( t \) be the number of T-shirts that Michael bought. We can set up the following equations based on the information given:

1. The total number of shirts is 7: \[ p + t = 7 \]

2. The total cost of the shirts is $131: \[ 28p + 15t = 131 \]

Now we can solve this system of equations.

From the first equation, we can express \( t \) in terms of \( p \): \[ t = 7 - p \]

Now substitute \( t \) in the second equation: \[ 28p + 15(7 - p) = 131 \]

Distribute: \[ 28p + 105 - 15p = 131 \]

Combine like terms: \[ 13p + 105 = 131 \]

Subtract 105 from both sides: \[ 13p = 26 \]

Now divide by 13: \[ p = 2 \]

Now substitute back to find \( t \): \[ t = 7 - p = 7 - 2 = 5 \]

Thus, Michael bought 2 polo shirts and 5 T-shirts.

The correct response is 2 Polos and 5 T-shirts.