Question

Gerard bought 9 hamburgers and 3 orders of fries for 24.75. Chris bought 6 hamburgers and 4 orders of fries for 19.50. Each hamburger cost the same amount. Each Order of fries cost the same amount. Wrote a system of equations that can be used to find how much one hamburger and one Order of fries cost.

Answer 1

9h + 3f = 24.75....multiply by 4
6h + 4f = 19.50 ...multiply by -3
----------------------
36h + 12f = 99 (result of multiplying by 4)
-18h - 12f = - 58.50 (result of multiplying by -3)
--------------------add
18h = 40.50
h = 40.50/18
h = 2.25 <== hamburgers cost 2.25 each

6h + 4f = 19.50
6(2.25) + 4f = 19.50
13.50 + 4f = 19.50
4f = 19.50 - 13.50
4f = 6
f = 6/4
f = 1.50 <== fries cost 1.50 per order

Answer 2

System of equations:

9x+3y=24.75

6x+4y=19.50

x: cost of a hamburger

y: cost of an order of fries

Explanation:

We define the variables of the system of equations:

x: cost of a hamburger

y: cost of an order of fries

We propose the system of equations:

To Gerard: 9x+3y=24.75

To Chris: 6x+4y=19.50

where, the coefficients in the equations represent the quantity that was purchased from each product and the variables represent the costs of each product.