math help cant quite figure it out

Question

1.     At the football game, 4 hotdogs and 2 sodas cost $8. The cost of 5 hotdogs and 3 drinks is $10.50. Determine the cost of a hotdog and the cost of a soda.

Answer 1

I am assuming drinks and sodas are the same thing, so I will call them both drinks.

I first translate this into math.

4 hotdogs and 2 drinks cost $8

4h+2d=8

5 hotdogs and 3 drinks cost $10.50

5h+3d=10.5

We then solve the first equation for a variable:

4h+2d=8

2d=8-4h

d=4-2h

Then we substitute this value for d into the second sentence.

5h+3(4-2h)=10.5

5h+12-6h=10.5

12-h=10.5

-h=-1.5

h=1.5

We then substitute this value for h back into one of the equations.

4(1.5)+2d=8

6+2d=8

2d=2

d=1

Hotd dogs are $1.50 and drinks are $1.