Question

The Booster Club voted on

where they would go for their
annual trip. A majority of the
club voted to go to a baseball
game. They bought 29 tickets.
Some of the tickets cost $21
each and some cost $27 each.
The total cost of all the tickets
was $675. How many tickets
of each price did they buy?

Answer 1

The number of tickets purchased costing $21 each = 18

The number of tickets purchased costing $ 27 each = 11

Explanation:

The total number of tickets purchased = 29

Here, let us assume that:

The number of tickets purchased costing $21 = m

The number of tickets purchased costing $ 27 = 29 - m

So, now the cost of m tickets costing $21 each = m x ( $21) = 21 m

Also, the cost of purchasing ( 29-m) tickets costing $27 each

= (29-m)x $27 = 783 - 27 m

Also, the total cost of purchasing 29 tickets = $ 675

⇒ The total cost of m tickets + (29- m ) tickets = $ 675

or, 21 m + 783 - 27 m = 675

⇒ - 6 m = 675 - 783 = -108

or, m 108/6 = 18

⇒ m = 18

Hence the number of tickets purchased costing $21 each = m = 18

The number of tickets purchased costing $ 27 each = 29 - m

= 29 - 18 = 11