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

To find the cost of 1 burger and 1 milkshake, set up a system of equations using the given information and solve for the variables.

Step-by-step explanation:

To find the cost of 1 burger and 1 milkshake, we can set up a system of equations based on the given information. Let's assign variables to represent the cost of a burger and a milkshake. Let x be the cost of 1 burger and y be the cost of 1 milkshake.

From the first statement, we can write the equation 2x + 3y = 13.

From the second statement, we can write the equation 5x + 7y = 31.

Now, we can solve this system of equations using the method of substitution or elimination to find the values of x and y, which will give us the cost of 1 burger and 1 milkshake.

Answer 2

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