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?

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.