Question

A school is buying movie tickets for an excursion.

The school buys a total of 32 tickets. The cost of an adult ticket, a,

is $12.50 and the cost of a student ticket, s, is $8.50. The total

cost of the tickets is $288. Which equations could be used to

find the number of each type of ticket purchased?

Answer 1

See below.

Explanation:

Two types of tickets are adult(a) and student(s). Let a and s stand for the numbers of tickets bought for each.

We know that a + s = 32 {The school buys a total of 32 tickets.}

The total cost is $288, made up of:

a*($12.50) and s*($8.50)

Thus, we can write:

a*($12.50) + s*($8.50) = $288

The two equations:

a + s = 32

a*($12.50) + s*($8.50) = $288

are all we need to calculate the numbers of a and s tickets.

===

a = 32-s

a*(12.50) + s*(8.50) = 288

(32-s)*(12.50) + s*(8.50) = 288

400 - 4s = 288

-4s = -112

s = 28 tickets

---

a + s = 32

a + 28 = 32

a = 4 tickets

==

Check:

tickets Price Total

a 4 $12.5 $50

2 28 $8.5 $238

$288