Question

The school that Stefan goes to is selling tickets to a choral performance. On the first day of ticket sales the school sold 3 senior citizen and 1 child ticket for a total of $38. The school took in $52 on the second day by selling 3 senior tickets and 2 child tickets. Find the price of a senior citizen ticket and the price of a child ticket.

Answer 1

The price of senior citizen ticket is $8 and that of children ticket is $14          

Solution:

Let the price of ticket for senior citizen be ‘s’ and for child be ‘c’

Given that on the first day of ticket sales the school sold 3 senior citizen and 1 child ticket for a total of $38

So, an equation can formed which is as follows:

3s + c = 38  ---- eqn 1

On the Second day of ticket sales the school sold 3 senior citizen and 2 child ticket for a total of $52

3s + 2c = 52  ---- eqn 2

Multiply eqn 1 by 2

6s + 2c = 76 ---- eqn 3

Now subtract eqn 2 from eqn 2

6s + 2c = 76

(-) 3s + 2c = 52

---------------------

3s = 24

s = 8

Plug in s = 8 in eqn 2,

24 + 2c = 52

2c = 28

c = 14

Hence, the price of senior citizen ticket is $8 and that of children ticket is $14