How much does a hotdog cost?

Question

Two burgers and one hotdog cost $4.82 at the same price, one burger and two hotdogs cost $3.70. How much does a hotdog cost?

Answer 1

Let b be the number of burgers and h be the number of hotdogs, then

2b+h=4.82

1b+2h=3.70

Since they are asking for the price of the hotdog, you want to get rid of the variable b. You can do that by multiplying the second equation by -2 (that way you have 2 and -2 for the coefficients of b and when you add 2 and -2 you get 0) and then adding the two equations

2b+h=4.82

-2b-4h=-7.40

+------------------------

-3h=-2.58

then divide both sides by -3

h=.86