Answer: price of a senior citizen ticket = $3.71
Let the price of a child ticket = $4.43
Explanation:
Let the price of a senior citizen ticket = x
Let the price of a child ticket = y
On the first day of ticket sales the school sold 22 senior citizen tickets and 10 child tickets for a total of $126. This will be:
22x + 10y = 126 ............ i
The school took in $51 on the second day by selling 3 senior citizen tickets and 9 child tickets. This will be:
3x + 9y = 51 ........... ii
22x + 10y = 126 ............ i
3x + 9y = 51 ........... ii
Multiply equation i by 3
Multiply equation ii by 22
66x + 30y = 378 ....... iii
66x + 198y = 1122 ........ iv
Subtract iii from iv
168y = 744
y = 744/168
y = 4.43
Since 3x + 9y = 51
3x + 9(4.43) = 51
3x + 39.87 = 51
3x = 51 - 39.87
3x = 11.13
x = 11.13/3
x = 3.71