Question

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

Answer 1

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`