Question 424727: Children's tickets to a movie cost $4. Adult tickets cost $7. If 275 tickets were sold for a total cost of $1174, how many of each type were sold?
Found 4 solutions by mananth, ikleyn, josgarithmetic, greenestamps:
Answer by mananth(16949)   (Show Source):
You can put this solution on YOUR website! children's ticket x numbers
adult ticket y numbers
...
x+y=275 .............1
4x+7y=1175 .............2
multiply (1)by -7
Multiply (2) by 1
-7x-7y=-1925
4x+7y=1175
Add the two equations
-3x=-750
/-3
x=250 children's tickets
plug value of x in (1) 1 x + 1
y=275
250+y=275
y=275-250
y=25 adult tickets
Answer by ikleyn(53751)  (Show Source):
You can put this solution on YOUR website! .
Children's tickets to a movie cost $4. Adult tickets cost $7.
If 275 tickets were sold for a total cost of $1174, how many of each type were sold?
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The solution by @mananth in his post is INCORRECT.
The problem is posed INCORRECTLY and has no solution.
I came to explain WHY it is so.
Let x be the number of adult tickets.
Then the number of children tickets is (275-x).
Write the total cost equation (same as the total revenue)
7x + 4*(275-x) = 1174 dollars.
Simplify and find x
7x + 4*275 - 4x = 1174,
7x - 4x = 1174 - 4*275
3x = 74
x = 74/3 = 24 <<<---=== ? ? ? ? ? ? ?
We got a CONTRADICTION: the number of tickets must be integer, but we obtained non-integer answer.
It means that the problem is posed INCORRECTLY and describes a situation
which NEVER may happen.
The solution by @mananth in his post is INCORRECT.
Simply IGNORE his solution.
Answer by josgarithmetic(39792)  (Show Source):
Answer by greenestamps(13327)  (Show Source):
You can put this solution on YOUR website!
This kind of problem can be solved quickly using logical reasoning and simple arithmetic.
If all 275 tickets were children's tickets, the total cost would be 275($4) = $1100; the actual total is $1174, which is $74 more.
The difference in the cost of an adult ticket and a children's ticket is $3, so the number of adult tickets should be $74/$3.
But that is not a whole number....
That means the numbers given in the problem cannot be correct.
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