Let x represent the number of adult tickets sold
Let y represent the number of student tickets sold
We were told that they sold 345 tickets altogether. This means that
x + y = 345
Adult tickets cost $3.50, student tickets are 2.50, If they made 1057.5 in total, then the equation representing this statement is
3.5x + 2.5y = 1057.5
Thus, the system of equations is
x + y = 345
3.5x + 2.5y = 1057.5
If these equations are plotted on a graph, the intersection points would be that x and y values corresponding to the point where both lines intersect. These are the solutions of the equations.
We can solve for them as shown below
By substituting x = 345 - y into 3.5x + 2.5y = 1057.5, it becomes
3.5(345 - y) + 2.5y = 1057.5
1207.5 - 3.5y + 2.5 = 1057.5
- 3.5y + 2.5 = 1057.5 - 1207.5
- y = - 150
y = 150
x = 345 - y = 345 - 150
x = 195
Thus, at the point of intersection, x = 195 and y = 150
The intersection point is the point where we can get the number of adult and student tickets that were sold