Question

Kim’s school is selling tickets for a play. On the first day of ticket sales the school sold 7 seniors citizen tickets and 14 student tickets for a total of $133. The school took in $89 on the second day by selling 8 senior citizen tickets and 7 student tickets. Find the price of a senior citizen ticket and the price of a student tickets.

Answer 1

The cost of one senior citizen ticket is $5

The cost of one student ticket $7

Explanation:

Let the cost of one senior citizen ticket be x and the cost of one student ticket be y

First day :

Number of senior citizen ticket sold = 7

Number of student ticket sold = 14

Told amount earned = $133

So the equation will be,

7x + 14y = 133 ------------(1)

Second day :

Number of senior citizen ticket sold = 8

Number of student ticket sold = 7

Told amount eared = $89

8x + 7y = 89-----------------------(2)

Multiplying equation (2) by 2

16x + 14y = 178----------------------(3)

Solving (1) and (3)

16x + 14y = 178

7x + 14y = 133

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

9x = 45

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

`x = (45)/(9)`

x= 5

Now substituting the x value in eq(1)

7(5) +14y = 133

35 +14y = 133

14y = 133 -35

14y = 98

`y = (98)/(14)`

y = 7