how much does eavh item cost individually?

Question

Alicia bought 2 burgers and 3 small fries at Dave’s Burger Shack for a total of $21.18. Jack bought 4 burgers and 2 small fries for a total of $29.56.

Answer 1

Hi Ariana,

If you set up the equations, with B for the price of the burgers, and F for the price of the fries.

you can use:

Alicia, 3B + 3F = 21.18 >>>> -6B - 6F = 21.18

>>>>> -6B + 12B - 6F + 6F = 21.18 + 29.56

Jack, 4B + 2F = 29.56 >>>> 12B +6F = 29.56

>>> if you multiple Alicia's equation by -2

and >>> you multiple Jack's equation by 3

Can you solve for B now? and then use your result to find F?

How did you do?

Julie

Answer 2

We are going to need to define some terms for this. Let's say the price of burgers is defined by x and the price of small fries is defined by y.

Next, we are to set some equations up. Since Alicia bought 2 burgers and 3 small fries, which totaled out for $21.18, the equation is 2x + 3y = 21.18. Since Jack bought 4 burgers and 2 small fries for $29.56, the equation will be 4x + 2y = 29.56.

Now that we set up the equations for this problem, we are to either solve for x or for y. Let's solve for y. Let's start with Alicia:

2x + 3y = 21.18

3y = 21.18 - 2x

y = 7.06 - (2/3)x

Now that we solved for y, let's plug the answer in for x for the second equation:

4x + 2y = 29.56

4x + 2(7.06 - (2/3)x) = 29.56

4x + 14.12 - (4/3)x = 29.56

(8/3)x + 14.12 = 29.56

(8/3)x = 29.56

x = 5.79

We have now solved for x, which means we found out how much burgers cost, which is $5.79. We now plug x back in the equation y = 7.06 - (2/3)x as follows:

y = 7.06 - (2/3)x

y = 7.06 - (2/3)(5.79)

y = 7.06 - 3.86

y = 3.20

We have now solved for y as well, which means we found out how much small fries cost, which is $3.20.

Therefore, one burger costs $5.79 and one small fry costs $3.20.