Math - Cindy, Tuesday, April 29, 2014 at 8:44pm

At Bobs diner, it costs $8.00 to purchase two hamburgers and one order of fries. The "family pack" costs 30.00 and comes with six hamburgers and six orders of fries. If the prices are constant,how much does one hamburger cost? Use system of equations to solve.

2H + 1F = 8 ===> F = 8-2H

6H + 6F = 30 or H+F=5

using substitution:
H + F = 5
H + 8-2H = 5
-H = -3
H = 3
then F = 8-6 = 2

each hamburger costs $3.00 and each fries costs $2.00

To solve this problem using a system of equations, let's assume the cost of one hamburger is "h" and the cost of one order of fries is "f."

According to the given information:
2h + f = 8.00 (equation 1) - Since purchasing two hamburgers and one order of fries costs $8.00.
6h + 6f = 30.00 (equation 2) - Since the family pack comes with six hamburgers and six orders of fries, and it costs $30.00.

Now, we have a system of equations with two variables. We can solve this system using either the substitution or elimination method.

Let's solve it using the elimination method:

Multiply equation 1 by 6 to make the coefficient of "h" in equation 1 the same as the coefficient of "h" in equation 2.
12h + 6f = 48.00 (equation 3)

Next, subtract equation 2 from equation 3 to eliminate the "f" term.
(12h + 6f) - (6h + 6f) = 48.00 - 30.00

Simplifying this, we get:
6h = 18.00

To find the value of "h" (the cost of one hamburger), divide both sides of the equation by 6:
h = 18.00 / 6
h = 3.00

Therefore, one hamburger costs $3.00.

So, the answer is that one hamburger costs $3.00.