Question

The booster club is selling refreshments. The following system of linear equations models the concession stand prices. Let represent the cost of a hot dog and represent the cost of the soda. Write the answers in decimal form. Solve the system of linear equations.

4h+4s=10

7h+5s=15

Answer 1

To solve the system of linear equations, we need to use the substitution or elimination method. Let's use the elimination method in this case.

Multiply the first equation by 5 and the second equation by -4 to make the coefficients of either h or s the same but with opposite signs:

First equation:
5(4h + 4s) = 5(10)
20h + 20s = 50

Second equation:
-4(7h + 5s) = -4(15)
-28h - 20s = -60

Now, we add the two equations to eliminate variable s:

20h + 20s = 50
-28h - 20s = -60
_________________
-8h = -10

Divide both sides by -8:
h = -10/-8
h = 1.25

Now, substitute the value of h back into the first equation to solve for s:
4(1.25) + 4s = 10
5 + 4s = 10
4s = 5
s = 5/4
s = 1.25

Therefore, the cost of a hot dog is $1.25 and the cost of a soda is $1.25.