SOLUTION: Fundraising. The St. Mark’s Community Barbecue served 250 dinners. A child’s plate cost $3.50 and an adult’s plate cost $7.00. A total of $1347.50 was collected. How many of each t

Algebra ->  Algebra  -> Coordinate Systems and Linear Equations -> SOLUTION: Fundraising. The St. Mark’s Community Barbecue served 250 dinners. A child’s plate cost $3.50 and an adult’s plate cost $7.00. A total of $1347.50 was collected. How many of each t      Log On

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Question 153024: Fundraising. The St. Mark’s Community Barbecue served 250 dinners. A child’s plate cost $3.50 and an adult’s plate cost $7.00. A total of $1347.50 was collected. How many of each type of plate was served?


Answer by orca(409) About Me  (Show Source):
You can put this solution on YOUR website!
Let x be the number of children.
Let y be the number of adults.
As the total number of dinners is 250, we have:
x + y = 250 ...................(1)
The amount of money from children: 3.5x
The amount of money from adults: 7y.
As the total is 1347.5,we have:
3.5x + 7y = 1347.5 ............(2)
Solving equations (1) and (2) simultaneously, we obtain:
x = 115
y = 135
So the numbers of children and adults are 115 and 135 respectively.
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How to solve
x + y = 250 .................(1)
3.5x + 7y = 1347.5...........(2)
From (1), we get x = 250 - y. Substitute it into equation (2), we obtain:
3.5(250 - y) + 7y = 1347.5
875 - 3.5y + 7y = 1347.5
875 + 3.5y = 1347.5
3.5y = 472.5
y = 135
x= 250 - y = 115