Ok, let's analyze what the question is telling us. From what I see, there are two important statements - "sold a total of 530 tickets" and "the total amount collected was $1740". Now let's think about how we can represent these using the variables given to us.
Well, we know the number of tickets can just be represented by totalling the number of children tickets and adult tickets sold. So we can write:
c + a = 530
We also know how much each ticket is worth (child - $3, adult -$4), and we can calculate the total amount of money made by multiplying the amount of money each ticket is worth by the number of tickets sold. So we can say the total amount for the children's tickets is 3c and the total amount of adult tickets is 4a. So the total can be represented by:
The system of equations can be used to solve this problem. C is child ticket and a is adult ticket.
Equation 1
3c+4a=1740
This equation comes from the cost of the tickets. 3c is the cost of $3 per child ticket and 4a is the cost of $4 per adult ticket. 1740 is the total amount collected.
Equation 2
c+a=530
This comes from the number of tickets sold. The c+a is the total of child and adult tickets sold and 530 is the total amount of tickets.
