The total price of a shirt and a cap is $11. If the price of the shirt was doubled and the price of the cap was three times its original price, the total price of a shirt and a cap would be $25. The following system of equations models this scenario:

x + y = 11
2x + 3y = 25

What is the price of each shirt and cap?

The price of a shirt is $9, and the price of a cap is $2.
The price of a shirt is $10, and the price of a cap is $1.
The price of a shirt is $8, and the price of a cap is $3.
The price of a shirt is $7, and the price of a cap is $4.

1 answer

To solve this system of equations, we can first solve for one variable in terms of the other from the first equation:

x = 11 - y

Then we can substitute this expression into the second equation:

2(11 - y) + 3y = 25
22 - 2y + 3y = 25
22 + y = 25
y = 3

Now that we have the price of the cap, we can substitute y = 3 back into the first equation to find the price of the shirt:

x + 3 = 11
x = 8

Therefore, the price of a shirt is $8, and the price of a cap is $3. The correct answer is:

The price of a shirt is $8, and the price of a cap is $3.