At a local baseball game, the concession stand has two different meal choices.

Question

At a local baseball game, the concession stand has two different meal choices. You can get 8 hotdogs and 5 drinks for $15.50 or you can get 3 hotdogs and 7 drinks for $13.50. If the price of hotdogs and drinks is the same for each meal, find how much it costs for an individual hotdog and an individual drink.

$ per hotdog.

$ per drink.

Answer 1

8h + 5d = 15.50

3h + 7d = 13.50

The easiest method to solve this problem is by using Cramer's Rule. This means using determinants to solve the system of equations.

H = (7 * 15.50 - 5 * 13.50) / 41

D = (8 * 13.50 - 3 * 15.50) / 41

The denominator in Cramer's Rule is always 41.

H = 1$

D = 1.50$

Answer 2

8H + 5D = 15.50

3H + 7D = 13.50

Because of the coefficients, this is a nuisance set to solve; neither elimination nor substitution is easy.

Probably the simplest way is to use Cramer's Rule (determinants).

The denominator in Cramer's Rule is 41.

Then H= (7*15.50-5*13.50)/41 and D=(8*13.50-3*15.50)/41.