Question

Burger Joint is celebrating their grand opening. For 2 milkshakes and 3 burgers, the cost is $13. For 5
milkshakes and 7 burgers, the cost is $31.
What is the cost of 1 burger and 1 milkshake?

Answer 1

For this case we propose a system of equations:

x: Let the variable representing the cost of a milkshake

y: Let the variable representing the cost of a burger

According to the statement we have:

$2x + 3y = 13\\5x + 7y = 31$

We multiply the first equation by -5:

$-10x-15y = -65$

We multiply the second equation by 2:

$10x + 14y = 62$

We have the following equivalent system:

$-10x-15y = -65\\10x + 14y = 62$

We add the equations:

$-10x + 10x-15y + 14y = -65 + 62\\-y = -3\\y = 3$

Thus, the cost of a burger is $3.

$2x + 3 (3) = 13\\2x + 9 = 13\\2x = 13-9\\2x = 4\\x = \frac {4} {2}\\x = 2$

So, the cost of a milkshake is $2

Answer:

Burger: $3

Milkshake: $2