Question 55428: I need help with these two word problems. I can not figure them out.
1. Adult tickets for a play cost $4 and child tickets cost $1. If there were 23 people at a performance and the theater collected $80 from ticket sales, how many children attended the play?
2.Tickets for an event cost $4 for children, $12 for adults, and $7 for senior citizens. The total ticket sales were $1920. There were 50 more adult tickets sold than child tickets, and the number of senior citizens tickets were 4 times the number of child tickets. How many of each ticket were sold?
Answer by piyu(4)   (Show Source):
You can put this solution on YOUR website! 1. Adult tickets for a play cost $4 and child tickets cost $1. If there were 23 people at a performance and the theater collected $80 from ticket sales, how many children attended the play?
ANS:
let the no. of adults be x and the no. of children be y
the total no. of people who attended the play = 23
which means x+y=23
the cost of an adult ticketis $4 and hence the total collections from adult tickets=4x
similarly the total collections from child tickets is $1 per child= y
the total colltecions is $80. which implies
4x+y=80. solving the system of linear equations
4x+y=80
x+y=23
we get y=4 (i.e) the no. of children who attended the play is 4
2.Tickets for an event cost $4 for children, $12 for adults, and $7 for senior citizens. The total ticket sales were $1920. There were 50 more adult tickets sold than child tickets, and the number of senior citizens tickets were 4 times the number of child tickets. How many of each ticket were sold?
ANS:
assume the no. of childern to be x, no. of adults to be y and the no. of senior citizens to be z.
the cost per ticket is $4 for children, $12 for adults, and $7 for senior citizens. the total ticket sales amounted to $1920. which is nothing but
4x+12y+7z=1920 (equation 1)
given that 50 more adult tickets were sold than child tickets
y-x=50 or y=50-x (equation 2)
the number of senior citizens tickets were 4 times the number of child tickets.
z=4x (equation 3)
4x+12y+7z=1920(from equation 1)
substituting for y and z from equations 2&3, we have
4x+12(x+50)+7(4x)=1920
4x+12x+600+28x =1920
44x+600 =1920
44x=1920-600
44x=1320
x=1320/44
x=30
from equation 2
y=50+x (i.e)y=50+30
y=80
from equation 3
z=4x or z=4(30)
z=120
hence the no. of child tickets sold is 30, no. of adult tickets sold is 80 and the no. of senior citizen tickets sold is 120
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