Let's define the next variables:
x: price of one senior ticket
y: the price of one child ticket
On the first day of ticket sales, the school sold 8 senior citizen tickets and 5 child tickets for a total of $94. That is:
8x + 5y = 94 (eq. 1)
The school took in $152 on the second day by selling 4 senior citizen tickets and 10 child tickets. That is:
4x + 10y = 152 (eq. 2)
Multiplying equation 2 by 2, we get:
2(4x + 10y) = 2*152
8x + 20y = 304 (eq. 3)
Subtracting equation 1 to equation 3, we get:
8x + 20y = 304
-
8x + 5y = 94
------------------------
15y = 210
y = 210/15
y = 14
Substituting this result into equation 1:
8x + 5(14) = 94
8x + 70 = 94
8x = 94 - 70
8x = 24
x = 24/8
x = 3
Each senior citizen ticket cost $3 and each child ticket cost $14