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Question 838895: At a college function, a total of 180 tickets were sold. The tickets were priced at $5, $10, and $15, and the money collected that day was $1,900. The sum of the numbers of $5 and $15 tickets sold was twice the number of $10 tickets sold. Find the number of each type of ticket sold for the college function.
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Answer by mananth(16946)   (Show Source):
You can put this solution on YOUR website! At a college function, a total of 180 tickets were sold. The tickets were priced at $5, $10, and $15, and the money collected that day was $1,900. The sum of the numbers of $5 and $15 tickets sold was twice the number of $10 tickets sold. Find the number of each type of ticket sold for the college function.
$5----------x numbers
$10---------y
$15---------z
x+y+z=180
5x+10y+15z= 1900
sum of $5 and $15 tickets = twice $10
x+z= 2y
x+y+z=180
x+z=2y
2y+y=180
3y= 180
y=60, number of $10 tickets
5x+10y+15z= 1900
5x+10*60+15z=1900
5x+600+15z=1900
5x+15z=1300
/5
x+3z=260
But x+z=120
120+2z=260
2z=260-120
2z=140
z=70 Number of $15 tickets
Balance $ 5 tickets
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