Question

725 tickets were sold for a game for a total of $1,487.50. If adult tickets sold for $2.50 and children's tickets sold for $1.50, how many of each kind of ticket were sold?

Answer 1

Answer: 400 adult tickets and 325 children's tickets were sold.

Step-by-step explanation:

Let x represent the number of adult tickets that were sold.

Let y represent the number of children's tickets tickets that were sold.

725 tickets were sold for the game. It means that

x + y = 725

If adult tickets sold for $2.500 and children's tickets sold for $1.50 and the total amount for which the tickets were sold $1,487.50, it means that

2.5x + 1.5y = 1487.50- - - - - - - - -1

Substituting x = 725 - y into equation 1, it becomes

2.5(725 - y) + 1.5y = 1487.50

1812.5 - 2.5y + 1.5y = 1487.50

- 2.5y + 1.5y = 1487.50 - 1812.5

- y = - 325

y = 325

x = 725 - y = 725 - 325

x = 400

Answer 2

Answer:

• 400 adult tickets
• 325 children's tickets

Step-by-step explanation:

Let x represent the number of adult tickets sold. Then 725-x is the number of children's tickets sold, and the total revenue is ...

  2.50x +1.50(725 -x) = 1487.50

  1.00x + 1087.50 = 1487.50 . . . . . eliminate parentheses

  x = 400 . . . . . . . . . . . . . . . . . . . . . subtract 1087.50

There were 400 adult tickets and 325 children's tickets sold.