Answer:
Adult tickets sold: 200
Children's tickets sold: 375
Explanation:
Set up equations
1.5x + 1y = 675
We got this equation because if we multiply the cost of the adult ticket with how many were sold, we get the total cost for adults. Since we don't know how many adult tickets were sold, we use x to represent that unknown value. $1.50x -> 1.5x
Same logic for the children's ticket, but since the amount of adult tickets and children's tickets may not be the same, we use a different variable, and in my example I will use y. $1y. We can simplify this to y.
If we add 1.5x to y, we should get the total cost, which is $675, so one of our equations looks like
1.5x + y = 675
For our next equation, we have:
x + y = 575
if x is the amount of adult tickets and y is the amount of children's tickets, the sum of these should be 575, as given by the problem.
Subtract
x + y = 575
from
1.5x + y = 675
1.5x + y = 675
x + y =575
1.5x-x= 0.5x y-y=0 675-575=100
0.5x + 0 = 100
0.5x = 100
x=200
Now that we have the amount of adult tickets (200, plug this into either of our earlier equations.
x + y = 575 would be easier to plug into
200 + y = 575
y = 375
So the amount of adult tickets sold is 200 and the amount of children's tickets sold is 375.