SOLUTION: Im having trouble solving this problem and ones like it. What is the answer and how is it found? If you buy 3 hotdogs and 3 sodas on your first trip to the concession stand and sp

Algebra ->  Finance -> SOLUTION: Im having trouble solving this problem and ones like it. What is the answer and how is it found? If you buy 3 hotdogs and 3 sodas on your first trip to the concession stand and sp      Log On


   

Question 283728: Im having trouble solving this problem and ones like it. What is the answer and how is it found?
If you buy 3 hotdogs and 3 sodas on your first trip to the concession stand and spend $22.50. You then go back a second time and spend $24 and buy 5 sodas and 2 hotdogs. How much does each hotdog cost and how much does each soda cost?
Found 2 solutions by richwmiller, scott8148:
Answer by richwmiller(17219) About Me  (Show Source):
You can put this solution on YOUR website!
3s+3h=2250
5s+2h=2400
so we have two equations with two unknowns.
we can solve by substitution or elimination(aka addition)
lets try elimination
multiply the first equation by -2 and the second by 3
-6s-6h=-4500
15s+6h=7200
add them
9s=2700
s=300
plug 300 for s in any equation and solve for h
3s+3h=2250
3*300+3h=2250
900+3h=2250
3h=1350
h=450
s=300

Answer by scott8148(6628) About Me  (Show Source):
You can put this solution on YOUR website!
3h + 3s = 22.50 ___ multiplying by 2 ___ 6h + 6s = 45.00

2h + 5s = 24.00 ___ multiplying by 3 ___ 6h + 15s = 72.00

subtracting ___ 9s = 27.00 ___ s = 3.00

substituting ___ 2h + 5(3.00) = 24.00 ___ 2h = 9.00 ___ h = 4.50