Question

3. Matt bought 12 packages of hot dogs and hamburgers for a barbecue. Let x represent the number of packages of hot dogs, which cost $2.75 each. Let y represent the number of packages of hamburgers, which cost $3.20 each. Matt spent a total of $35.25. Write and solve a system of equations that can be used to represent the amount of hot dogs and hamburger packages Matt bought. Are there any constraints on your variables? Is the solution viable or non-viable?

Answer 1

Matt bought 7 packages of hot dogs and 5 packages of hamburger.

Explanation:

We are given the following in the question

Let x represent the number of packages of hot dogs.

Cost of one packet of hot dog = $2.75

Let y represent the number of packages of hamburgers

Cost of one packet of hamburgers = $3.20

Then, we can write the following equations:

`x + y = 12\\2.75x + 3.2y = 35.25`

Solving the two equations,

`2.75x + 2.75y = 33\\2.75x + 3.2y = 35.25\\\Rightarrow 0.45y = 2.25\\y = 5\\x = 7`

Thus, Matt bought 7 packages of hot dogs and 5 packages of hamburger.

The solution is viable.

Constraints to the system of equation:

`x,y \geq 0 \\x + y = 12\\2.75x + 3.2y = 35.25`