Question

for the opening day of a carnival, 800 admission tickets were sold. The receipts totaled $3775. Tickets for children cost $3 each, tickets for adults cost $8 each, and tickets for senior citizens cost $5 each. There were twice as many children's tickets sold as adults. How many of each type of ticket were sold?

Answer 1

Total tickets sold = 800
Total revenue = $3775

Ticket costs:
$3 per child,
$8 per adult,
$5 per senior citizen.

Of those who bought tickets, let
x = number of children
y = number of adults
z = senior citizens

Therefore
x + y + z = 800 (1)
3x + 8y + 5z = 3775 (2)

Twice as many children's tickets were sold as adults. Therefore
x = 2y (3)

Substitute (3) into (1) and (2).
2y + y + z = 800, or
3y + z = 800, or
z = 800 - 3y (4)
3(2y) + 8y + 5z = 3775, or
14y + 5z = 3775 (5)

Substtute (4) nto (5).
14y + 5(800 - 3y) = 3775
-y = -225
y = 225
From (4), obtain
z = 800 - 3y = 125
From (3), obtain
x = 2y = 450

Answer:
The number of tickets sold was:
450 children,
225 adults,
125 senior citizens.