Question

On Tuesday Barney sold 5 hats and 3 shirts at the swap meet for $45. On Wednesday he sold 2 hats and 6 shirts for $42 ? How much did he sell each hat for? How much did he sell each shirt for?

Answer 1

Each hat was sold for $12 and each shirt for $-2.

Step-by-step explanation:

To find the price of each hat, we'll solve a system of equations using the given information.

Let's denote the price of a hat as 'h' and the price of a shirt as 's'.

From the first equation, we know that 5h + 3s = 45. From the second equation, we know that 2h + 6s = 42.

To solve this system of equations, we can use substitution or elimination. Here, we'll use substitution.

From the second equation, we can rewrite it as h = (42 - 6s) / 2.

Substituting h in the first equation, we get 5((42 - 6s) / 2) + 3s = 45.

Simplifying this equation, we get: 21 - 15s + 3s = 45. Combining like terms, we have -12s = 24. Dividing by -12, we get s = -2.

Substituting s = -2 back into the equation h = (42 - 6s) / 2, we get h = (42 - 6(-2)) / 2. Simplifying this equation, we have h = 12.

Therefore, Barney sold each hat for $12 and each shirt for $-2.