Question

The total price of a shirt and a cap is $12. 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 $26. The following system of equations models this scenario: x + y = 12 2x + 3y = 26 What is the price of each shirt and cap? The price of a shirt is $7, and the price of a cap is $5. The price of a shirt is $8, and the price of a cap is $4. The price of a shirt is $9, and the price of a cap is $3. The price of a shirt is $10, and the price of a cap is $2.

Answer 1

x = price of shirt = $10y = price of cap = $2

Answer 2

x = price of shirt = $10

y = price of cap = $2

Explanation:

x = price of shirt

y = price of cap

(1) x+y = 12

(2) 2x+3y = 26

x = 12-y substitute this into equation 2

2(12-y) + 3y = 26

24 - 2y + 3y = 26

y = 26-24 = 2 substitute this into equation 1

x+2 = 12

x = 12-2 = 10