Question 1197568: Ticket prices at an outdoor theater performance are $2.50 for children and $5.00 for adults. One evening, $6700 is collected from 1900 people attending. How many children and how many adults attend?
Found 3 solutions by MathLover1, math_tutor2020, MathTherapy:
Answer by MathLover1(20849)   (Show Source):
Answer by math_tutor2020(3816)  (Show Source):
You can put this solution on YOUR website!
c = number of children
1900-c = number of adults
Those two quantities add to 1900 total people.
2.50c = revenue from just the children only
5(1900-c) = 9500-5c = revenue from the adults only
2.50c+9500-5c = -2.50c+9500 = total revenue
-2.50c+9500 = 6700
-2.50c = 6700-9500
-2.50c = -2800
c = -2800/(-2.50)
c = 1120 is the number of children
which leads to
1900-c = 1900-1120 = 780 is the number of adults
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Check:
1120 children = 2.50*1120 = 2800 dollars in revenue
780 adults = 5*780 = 3900 dollars in revenue
2800+3900 = 6700 dollars total revenue
The revenue portion is confirmed.
The population count can be confirmed like this
1120 children + 780 adults = 1900 total people
Both key aspects (revenue and population) are confirmed.
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Answers:
1120 children and 780 adults
Answer by MathTherapy(10549)  (Show Source):
You can put this solution on YOUR website! Ticket prices at an outdoor theater performance are $2.50 for children and $5.00 for adults. One evening, $6700 is collected from 1900 people attending. How many children and how many adults attend?
Let number of adults be A
Then number of children = 1,900 - A
We then get the following PROCEEDS equation: 5A + 2.5(1,900 - A) = 6,700
A + .5(1,900 - A) = 1,340 ------ Factoring out/Dividing by GCF, 5
A + 950 - .5A = 1,340
A - .5A = 1,340 - 950
.5A = 390
Number of adults, or 
You should now be able to determine the number of children!
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