Question

The drama club sold a total of 140 tickets to their spring production. Adult tickets cost $8 each and student tickets cost $5. If the total amount sold was $760, how many adult tickets were sold? How many children tickets were sold? (Give the answer and the system of equations you used to solve this).

Answer 1

Total tickets sold = 140

So if the adult ticket is represented by a

and student ticket by s

then we can obtain the system of the equation since the price of the different tickets are known

Total ticket = a + s = 140 ------------------ Equation 1

The cost of adult tickets will be 8 x a = 8a

The cost of student tickets will be 5 x s = 5s

Then total cost = 8a + 5s = 760 ----------------------Equation 2

Solving the two equations simultaneously

Method: Solve Using Elimination Method

Multiply equation 1 by 8 so as to eliminate a

(a + s = 140 x ) =>

8a + 8s = 1120 ------- equation 3

8a + 5s = 760 --------- equation 2

Subtracting equation 2 from equation 3

8s - 5s = 1120 - 760

3s = 360

Divide both sides by 3

s = 360/3

s = 120

That means that 120 children tickets were sold

To get the number of adult tickets sold

We will substitute s = 120 into equation 1

a + s = 140

a + 120 = 140

a = 140 - 120

a = 20