What’s the answer

Question

At a concession stand,three hotdogs and four hamburgers cost $12.50;four hotdogs and three hamburgers cost $12.00. Find the cost of one hotdog and the cost of one hamburger.

Answer 1

These confused me at first, too!

3d + 4b = 12.5

4d + 3b = 12

We need either d or b to be opposites to cancel out. Let's multiply the top by 4 and the bottom by -3.

12d + 16b = 50

-12d - 9b = 36

Adding the equations together...

7b = 14

b = $2

I bet you can find the cost of a hotdog!

Answer 2

Let d = the price of a hotdog and b = the price of a hamburger:

3d+4b=12.50

4d+3b=12.00

Multiply the second equation by 4/3 and subtract from the first:

-7/3d=-3.50

d = 1.5

Substitute 1.5 in for d in the first equation

4.5 + 4b = 12.50

4b = 8

b = 2

1 hotdog costs $1.50

1 hamburger costs $2.00