SOLUTION: 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 an

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

RELATED QUESTIONS
Here is the word problem I need help with. Adult tickets for a play cost $17 and child (answered by stanbon,Paul)

I need help on this word problem. Thank You in advance for your help. Adult tickets... (answered by jim_thompson5910)

I need help with this problem i can't remember how to figure it out. Ticket sales for (answered by elima)

Erica paid $46 for 2 adult and 4 child tickets to a play. Karen paid $86 for 4 adult and (answered by josgarithmetic)

Sue paid $46 for 2 adult and 4 child tickets to a play. Karen paid $86 for 4 adult and 7... (answered by ankor@dixie-net.com)

Please help me with these two word problems. My head hurt from try to figure them out.... (answered by ankor@dixie-net.com)

Word Problem-- Adult tickets for a play cost $4 and child tickets costs $1. If there... (answered by checkley71)

Adult tickets for a play cost $17 and child tickets cost $8. If there were 24 people at... (answered by checkley71)

A total of 303 tickets were sold for the school play. The number of student tickets sold... (answered by checkley77,Mathtut)