Question 1166731: A movie theater advertises that a family of two adults, one student, and one child between the ages of 3 and 8 can attend a movie for $15. An adult ticket costs as much as the combined cost of a student ticket and a child ticket. You purchase 1 adult ticket, 4 student tickets, and 2 child tickets for $23. What is the price per ticket for a student ticket?
Found 2 solutions by Theo, ikleyn:
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! let A = the cost of an adult ticket.
let S = the cost of a student ticket.
let C = the cost of a child ticket.
your two formulas are:
2A + S + C = 15
A + 4S + 2C = 23
you are given A = S + C because one adult ticket is the same as the combined cost of a student and child ticket.
replace A in the two equations with S + C to get:
2 * (S + C) + S + C = 15
S + C + 4S + 2C = 23
simplify and combine like terms to get:
3S + 3C = 15
5S + 3C = 23
subtract the first equation from the second to get:
2S = 8
solve for S to get:
S = 4
in the first first equation of 3S + 3C = 15, replace S with 4 to get:
3 * 4 + 3C = 15
simplify to get:
12 + 3C = 15
subtract 12 from both sides of this equation and simpliy to get:
3C = 3
solve for C to get:
C = 1
you have:
S = 4
C = 1
since A = S + C, you also have:
A = 5
in your two original equations, replace A with 5 and S with 4 and C with 1 to get:
2A + S + C = 15 becomes 2*5 + 4 + 1 = 15 which becomes 15 = 15 which is true.
A + 4S + 2C = 23 becomes 5 + 4*4 + 2*1 = 23 which becomes 5 + 16 + 2 = 23 which becomes 23 = 23 which is also true.
this confirms the values for A and S and C are good.
your solution is that S = 4 which means that the price of a student ticket is 4 dollars.
Answer by ikleyn(52903)  (Show Source):
You can put this solution on YOUR website! .
The problem formulation in your post is made UNPROFESSIONALLY.
The first statement says that a certain combination of tickets is sold (or is ad) at a certain cost.
Then after that, you start reasoning about totally different combination of tickets.
So the story you try to bring to a reader, does not seem consistent.
There are MANY EXCESSIVE words in it - therefore it is unprofessional.
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