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. Three-fourths as many teenagers as children attended. How many adults attended?

Answer 1

Answer: 220

Explanation:

Children (x): $2

Teens (y): $3,
`(3)/(4)x`

Adults: (z): $5

Quantity: x + y + z = 570 ⇒ x +
`(3)/(4)x` + z = 570 ⇒ 1.75x + z = 570

Cost: 2x + 3y + 5z = 1950 ⇒ 2x + 3
`((3)/(4)x)` + 5z = 1950 ⇒ 2x + 2.25x + 5z = 1950 ⇒ 4.25x + 5z = 1950

Qty: 1.75x + z = 570 → 5(1.75x + z = 570) → 8.75x + 5z = 2850

Cost: 4.25x + 5z = 1950 → -1(4.25x + 5z = 1950 → -4.25x - 5z = -1950

4.50x = 900

x = 200

Teens (y):
`(3)/(4)x`

y =
`(3)/(4)(200)`

=
`(600)/(4)`

= 150

Quantity: x + y + z = 570

200 + 150 + z = 570

350 + z = 570

z = 220