SOLUTION: At a movie theater a family buys 2 adult tickets and 1 child ticket for a total of $18.00. Another family buys 1 adult ticket and 3 child tickets for a total of $21.50. What is a l

Question 857651: At a movie theater a family buys 2 adult tickets and 1 child ticket for a total of $18.00. Another family buys 1 adult ticket and 3 child tickets for a total of $21.50. What is a linear equation that can be used to determine the price of an adult ticket and the price of a child ticket?
Answer by JulietG(1812) (Show Source): You can put this solution on YOUR website!
2A + 1C = 18
1A + 3C = 21.50
Add them together
3A + 4C = 39.50
.
Here's my brain's way of going about it.
We know that an adult's ticket ends in .50 (the first equation is even; the second is odd).
We can assume that an adult ticket is priced higher than a child's. With that assumption...
We can tell that an adult ticket is no more than 7.50 and no less than 6.50.
Plug the values in to see:
2(6.50) + C = 18. C would be 5
2(7.50) + C = 18. C would be 3
Let's try the 7.50 into the second equation:
7.50 + 9 does not equal 21.50. Oops!
What about the other?
6.50 + 15 does equal 21.50. Success!
The adult ticket is $6.50 and the child's ticket is $5 (must be a matinee!)
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