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 (1st equation)

3h + 7d = 13.50 (2nd equation)

where h is the price of one hotdog and d is the price of one drink.

The idea behind the elimination method is to cancel one of the variables so that we are left with only one variable to solve for. Firstly, we can look at the d terms, which are 5d and 7d. Lets multiply the 1st equation by 7 and the 2nd equation by 5 so that both of them have 35d:

7[8h + 5d = 15.50] Multiply 1st equation by 7

5[3h + 7d = 13.50] Multiply 2nd equation by 5

_______________

56h + 35d = 108.50

15h + 35d = 67.50

_______________ Now subtract them so the d cancels

41h = 41.00 Divide by 41 on both sides to solve for h

h = 1.00

Now that we have the value of h, we can substitute it into the 1st equation or the 2nd equation to solve for d. Lets choose the 2nd equation since the numbers are smaller:

3h + 7d = 13.50 Plug in h = 1.00

3(1.00) + 7d = 13.50 Simplify

3 + 7d = 13.50 Subtract 3 on both sides

7d = 10.50 Divide by 7 on both sides to isolate d

d = 1.50

Lastly, we can plug both values back into the original equations to make sure they work:

8(1.00) + 5(1.50) = 8 + 7.50 = 15.50 (matches the 1st equation)

3(1.00) + 7(1.50) = 3 + 10.50 = 13.50 (matches the 2nd equation)

We have solved for both prices.

Hotdog = $1.00; Drink = $1.50

Answer 2

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 3

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.