At a baseball game, two pretzels and five hot dogs cost $31.25.
Four hot dogs and four pretzels cost $32.20. How much does each hot dog cost? How much does each pretzel cost?
Let's represent the cost of a hot dog as H and the cost of a pretzel as P.
We can form the following equations based on the given information:
2P + 5H = 31.25
4P + 4H = 32.20
To solve the system of equations, we can use the substitution method:
From the first equation:
2P + 5H = 31.25
2P = 31.25 - 5H
P = (31.25 - 5H)/2
Substitute P into the second equation:
4((31.25 - 5H)/2) + 4H = 32.20
62.5 - 10H + 4H = 32.20
-6H = -30.30
H = 5.05
Now we can substitute the value of H back into the first equation to solve for P:
2P + 5(5.05) = 31.25
2P + 25.25 = 31.25
2P = 6
P = 3
Therefore, each hot dog costs $5.05 and each pretzel costs $3.