Question 258311: Let's see if you guys can bail me out again tonight with another story problem. I actually have it solved (FINALLY), but will post my question at the end. The problem:
Movie tickets cost $25 for adults, and $5.00 for children. Last night a total of 305 tickets were sold totalling $6025, How many of each ticket was sold?
I was able to set up the first part of the equation with no problem, but I kept wanting the right side to be 305 instead of 6025.
It took me an hour to realize it should read:
c(5) + (305 - c)(25) = 6025
and NOT c(5) + (305 - c)(25) = 225
That just makes so much more sense to me. Am I not looking for the number of tickets?
Ive ran into this same problem numerous times. I can get the first part of the equation set up, then flounder helplessly with the back 1/2. In some problems both numbers are required ( as in 6025(305) ) and sometimes it's just one of the numbers...but I'm having a hard time figuring out which one! This is probably one of those deals where you either see it or you don't, but I hoped maybe someone would have some kind of pointer for me.
Thanks a million in advance!
La
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! Movie tickets cost $25 for adults, and $5.00 for children. Last night a total of 305 tickets were sold totalling $6025, How many of each ticket was sold?
let a = number of adult tickets sold.
let c = number of child tickets sold.
25 * a + 5 * c = 6025
a + c = 305
you have 2 equations that have to be solved simultaneously (same solution for both equations).
solve for a or c in the second equation and then use that to solve for the remaining variable in the first equation.
a + c = 305
solve for a to get:
a = 305 - c
substitute for a in the first equation.
first equation is:
25 * a + 5 * c = 6025
substitute 305 - c for a to get:
25 * (305 - c) + 5 * c = 6025
simplify to get:
7625 - 20*c = 6025
subtract 7625 from both sides of the equation to get:
-20*c = 6025 - 7625 = -1600
divide both sides of the equation by -20 to get:
c = -1600/-20 = 80
since a + c = 305, then a must be equal to 305 - 80 = 225
225 + 80 = 305
25 * 225 + 80 * 5 = 5625 + 400 = 6025
numbers look good.
answer is:
number of adult tickets is 225
number of child tickets is 80
the number of tickets sold is a + c = 305
the amount of money made is 25*a + 5*c = 6025
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