Question 1204764: At the local drive-in theater, the manager sold 200 tickets. Adult tickets cost $9 each, while children's tickets cost $5 each. If the theater sold $1420 worth of tickets, how many adult tickets and how many children's tickets were sold?
Found 3 solutions by mananth, Theo, greenestamps:
Answer by mananth(16946)   (Show Source):
You can put this solution on YOUR website! At the local drive-in theater, the manager sold 200 tickets. Adult tickets cost $9 each, while children's tickets cost $5 each. If the theater sold $1420 worth of tickets, how many adult tickets and how many children's tickets were sold?
Let number of adult tickets sold be x
and the number of child tickets be y
the manager sold 200 tickets.
x+y=200---------------------------------1
Adult tickets cost $9 each, while children's tickets cost $5 each. If the theater sold $1420 worth of tickets
Revenue from sales
9x+5y =1420------------------------------2
Multiply (1) by 5 and subtract from (2)
9x+5y =1420
5x+5y=1000
4x = 420
x = 420/4
x= 105 the number of adult tickets sold
you continue
Answer by Theo(13342)  (Show Source):
You can put this solution on YOUR website! a = number of adult tickets
c = number of child tickets.
your equations are:
a + c = 200
9a + 5c = 1420
multiply boh sides of the first equation by 9 and leave the second equation as is to get:
9a + 9c = 1800
9a + 5c = 1420
subtract the second equation from the first to get:
4c = 380
solve for c to get:
c = 380/4 = 95
a = 200 - 95 = 105
you have 105 adult tickets and 95 child tickets.
total cost is 9 * 105 + 5 * 95 = 1420.
numbers look good.
your solution is 105 adult and 95 child tickets were sold.
Answer by greenestamps(13200)  (Show Source):
You can put this solution on YOUR website!
The formal algebraic solutions provided by the other tutors are fine.
But you can get good mental exercise, and good problem-solving practice, by solving the problem using logical reasoning and simple mental arithmetic.
If all 200 tickets were children's tickets, the total cost would be 200($5) = $1000.
The actual total cost was $1420-$1000 = $420 more than that.
Each adult ticket costs $4 more than each children's ticket.
The number of adult tickets sold was $420/$4 = 105.
ANSWER: 105 adult tickets and 200-105 = 95 children's tickets.
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