Answer:
Price of Adult tickets =$ 13
Price of student tickets =$ 8
Explanation:
Lets us represent the price of adult tickets = x
The price of student tickets = y
On the first day of ticket sales the school sold 10 adult tickets and 13 student tickets for a total of $234.
= 10 × x + 13 × y = $234
= 10x + 13 y = 234
The school took in $97 on the second day by selling 5 adult tickets and 4 student tickets.
5 × x + 4 × y = $97
= 5x + 4y = 97
Hence:
10x + 13y = 234......Equation 1
5x + 4y = 97......... Equation 2
We solve by elimination method
Multiply the equation 1 by 5 and equation 2 by 10 which are the coefficient of x
10x + 13y = 234......Equation 1 × 5
5x + 4y = 97......... Equation 2 × 10
50x + 65y = 1170......Equation 3
50x + 40y = 970..... Equation 4
Subtract Equation 4 from Equation 3
25y = 200
y = 200/25
y = 8
Therefore the price of student ticket = $8
Note that
5x + 4y = 97......... Equation 2
5x + 4 × 8 = 97
5x = 97 + 32
5x = 65
x = 65/5
x = 13
Therefore price of adult tickets = $13