Question 1171918: Bob bought a popcorn, a soda, and a hotdog at the movies for $6.94. Popcorn costs $1 more than a hotdog. A soda costs $0.81 less than a hotdog. How much is each item?
Found 3 solutions by josgarithmetic, Theo, MathTherapy:
Answer by josgarithmetic(39616)   (Show Source):
Answer by Theo(13342)  (Show Source):
You can put this solution on YOUR website! p = price of a box of popcorn
s = price of one soda
h = price of one hotdog
t = total price
your equation is:
t = p + s + h
you are given that the price of a box of popcorn is 1 dollar more than the price of a hotdog.
the equation for that is:
p = h + 1
you are given that the price of a soda is .81 less than the price of a hotdog.
the equation for that is:
s = h - .81
the equations you have so far are:
t = p + s + h
p = h + 1
s = h - .81
what you want to do is reduce the number of unknowns in the equation of t = p + s + h down to 1.
then you can solve for that one unknown.
once you have that, you can use that value to solve for the rest of the unknowns.
looking at p = h + 1 and s = h - .81, it looks like h is in both of them.
we should be able to solve for p and s in terms of h.
we have p = h + 1 so we don't have to do anything with that because p is already solved for in terms of h.
we have s = h - .81 so we don't have to do anything with that because s is already solved for in terms of h.
in the equation of t = p + s + h, replace p with h + 1 and replace s with h - .81 to get:
t = p + s + h becomes:
t = (h + 1) + (h - .81) + h
simplify to get:
t = h + 1 + h - .81 + h
regroup the terms so that like terms are grouped together to get:
t = (h + h + h) + (1 - .81).
combine like terms to get:
t = 3h + .19
since t = 6.94, the equation becomes:
6.94 = 3h + .19
subtract .19 from both sides of the equation to get:
6.94 - .19 = 3h
simplify to get:
6.75 = 3h
solve for h to get:
h = 6.75 / 3 = 2.25
from s = h - .81, you get s = 2.25 - .81 which becomes:
s = 1.44
from p = h + 1, you get p = 2.25 + 1 which becomes:
p = 3.25
you now have:
p = 3.25
s = 1.44
h = 2.25
t = p + s + h becomes:
t = 3.25 + 1.44 + 2.25 = 6.94
this agrees with t is supposed to be, so the numbers for p and s and h look good.
your solution is that the price of a box of popcorn is 3.25 and the price of a soda is 1.44 and the price of a hotdog is 2.25.
Answer by MathTherapy(10551)  (Show Source):
You can put this solution on YOUR website!
Bob bought a popcorn, a soda, and a hotdog at the movies for $6.94. Popcorn costs $1 more than a hotdog. A soda costs $0.81 less than a hotdog. How much is each item?
Let cost of a hotdog be H
Then cost of a popcorn = H + 1
Also, cost of a soda = H - .81
We then get: H + H + 1 + H - .81 = 6.94
3H + .19 = 6.94
3H = 6.75
Cost of a hotdog, or 
Now, you can find the cost of a popcorn and of a soda!
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