Question 831673
Let the number of adults be x and the number of children be y 
We have the total number of both is 449 people, so we have the first equation:
x + y = 449
Then we have the total cost of adult is 12x ($12 each ticket times the number of  adults) and the total cost of children is 7y ($7 each ticket times the number of children) and the total cost of both is $4748 (given). So we have the second equation: 
12x + 7y = 4748
Now as we have 2 equations, we can form a system of equation and solve for x and y 
*[invoke linear_substitution "x", "y", 1, 1, 449, 12, 7, 4748 ]
You get x = 321 and y = 128
That means the number of adults are 321 and the number of children are 128 
That means there are 321 adult tickets bought and 128 children tickets bought
TA-DAH 
:D