Question

One week Chuck bought 2 packs of chicken and 3 packs of beef for $42.50. The next week he bought 5 packs of chicken and 6 packs of beef for $94.25. What is the price of each pack of chicken and each pack of beef?

Answer 1

Each pack of chicken costs $8 and each pack of beef costs $9.24.

Explanation:

This question can be solved using a system of equations:

I am going to say that:

x is the cost of each pack of chicken.

y is the cost of each pack of beef.

2 packs of chicken and 3 packs of beef for $42.50.

This means that
`2x + 3y = 42.50`

5 packs of chicken and 6 packs of beef for $94.25.

This means that
`5x + 6y = 94.25`

We have to solve the following system:

`2x + 3y = 42.50`

`5x + 6y = 94.25`

I will use the addition method, multiplying the first equation by -2, and adding to the second

`-4x - 6y = -85`

`5x + 6y = 94.25`

-4x + 5x - 6y + 6y = -85 + 94.24

x = 9.24.

And

`2x + 3y = 42.50`

`3y = 42.50 - 2x`

`y = (42.50 - 2*9.24)/(3)`

`y = 8`

Each pack of chicken costs $8 and each pack of beef costs $9.24.