The Walker and Baldwin families ordered lunch at the refreshment stand at the football game. The Walker family ordered 4 hot dogs, 3 veggie burgers, and 7 orders of French fries, and paid $36. The Baldwin family ordered 6 hot dogs, 2 veggie burgers, and 8 orders of French fries, and paid $39. If an order of French fries costs $1.75, what are the prices of a hot dog and a veggie burger?
Let's represent the cost of a hot dog as "h" and the cost of a veggie burger as "v".
From the information given, we can set up the following equations:
4h + 3v + 7(1.75) = 36
6h + 2v + 8(1.75) = 39
Simplifying the equations, we get:
4h + 3v + 12.25 = 36
6h + 2v + 14 = 39
Rearranging the equations, we have:
4h + 3v = 23.75
6h + 2v = 25
Now, we can solve these two equations simultaneously to find the values of h and v.
Multiplying the first equation by 2, we get:
8h + 6v = 47.5
Subtracting the second equation from this new equation, we get:
8h + 6v - 6h - 2v = 47.5 - 25
2h + 4v = 22.5
2(h + 2v = 22.5 / 2
h + 2v = 11.25
h = 11.25 - 2v
Substitute h = 11.25 - 2v into 4h + 3v = 23.75:
4(11.25 - 2v) + 3v = 23.75
45 - 8v + 3v = 23.75
-5v = -21.25
v = 4.25
Now substitute v back into h = 11.25 - 2v
h = 11.25 - 2(4.25)
h = 11.25 - 8.5
h = 2.75
Therefore, the price of a hot dog is $2.75 and the price of a veggie burger is $4.25.