A group of students go out to lunch. If they order two hamburgers and five hot dogs, the bill will be $8.00 If they order 5 hamburgers and 2 hot dogs the bill will be $9.50. What is the price of

Question

What is the price of a hamburger

Answer 1

Hi Jay,

Well the first order suggests the equation:

2H + 5D = 8 H is a hamburger, D is a hot dog

The second order suggests the equation:

5H + 2D = 9.5

Suppose make the first order twice, so the total order is:

4H + 10D = 16

And we make the second order 5 times, then it's total order is:

25H + 10D = 47.5

Now, each of the orders has 10 hot dogs. Let us subtract the smaller order and cost from the other. It leaves

21H = 31.5 Then Divide by 21

H = 1.5

A hamburger costs $1.50

This is called the elimination (or sometimes addition) method of solving a system of equations. The trick is choosing to multiply each order by a number that will leave you with a number of, in this case, hot dogs, that is the same as in the other order.

Answer 2

2h + 5d = 8.00

5h + 2d = 9.50

Can you solve by elimination and answer?