Question 1171918
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.