Question

Mozza’s cheese supplies sells six mozzarella cheeses and eight Swiss cheeses to Munga’s deli for $83.60, and four mozzarella cheeses and four Swiss cheeses to Mina’s deli for $48. How much does each type of cheese cost?

Answer 1

Hello!

The first thing to do is create variables. Say s = price of swiss cheese, and m = price of mozzarella.

Now, create your equations based off of the two statements given.

Six mozzarella cheeses and eight Swiss cheeses to Munga’s deli for $83.60: 6m + 8s = 83.6

Four mozzarella cheeses and four Swiss cheeses to Mina’s deli for $48: 4m + 4s = 48

Now, form your system of equations.

$\left \{ {{6m+8s=83.6} \atop {4m + 4s = 48}} \right.$

To solve this, I'm going to use elimination. This multiplies one of the equations by a certain factor, and allows the two equations to be cancelled out. That was not the best explanation, but hopefully this should help:

Multiply the bottom equation by -2 so the 2 "s's" can cancel out.

$\left \{ {{6m+8s=83.6} \atop {4m + 4s = 48}} \right.$

$\left \{ {{6m+8s=83.6} \atop {-8m - 8s = -96}} \right.$

Now, add the bottom equation to the top. There is no good way to write this out in this text box, so I'll explain it - what you're doing is you're adding the individual components; add together what's on the left side of both equations, and what's on the right side of both equations.

(6m + 8s = 83.6) + (-8m - 8s = -96) -> 6m + 8s - 8m - 8s = 83.6 - 96

Now solve for m.

6m + 8s - 8m - 8s = 83.6 - 96

6m - 8m = 83.6 - 96

-2m = -12.4

m = 6.2

Now, to get s, substitute m in into one of the original equations.

4m + 4s = 48

4(6.2) + 4s = 48

24.8 + 4s = 48

4s = 23.2

s = 5.8

Therefore, swiss cheese costs $5.80 and mozzarella $6.2.

Hope this helps!