181k views
2 votes
Tickets to a concert cost $2 for children, $3 for teenagers and $5 for adults. When 570 people attended the concert, the total ticket receipts were $1950. Compared to the number of children in attendance, three-fourths as many teenagers attended. How many teenagers attended?

a. 200
c. 220
b. 150
d. 316

1 Answer

4 votes

Let

x--------> the number of children

y------> the number of teenagers

z------> the number of adults

we know that


2x+3y+5z=1,950 ------> equation A


x+y+z=570 -----> equation B


y=(3)/(4)x


x=(4)/(3)y -------> equation C

Substitute equation C in equation A and equation B


2[(4)/(3)y]+3y+5z=1,950


(17)/(3)y+5z=1,950 --------> equation D


[(4)/(3)y]+y+z=570


(7)/(3)y+z=570 --------> equation E

Multiply equation E by
-5


-(35)/(3)y-5z=-2,850 --------> equation F

Adds equation D and equation F


(17)/(3)y+5z=1,950\\\\-(35)/(3)y-5z=-2,850\\\\---------\\\\-(18)/(3)y=-900\\\\y=3*900/18\\\\y=150\ teenagers

therefore

the answer is the option


150\ teenagers


User Mike Guthrie
by
7.1k points