The student council is sponsoring a carnival to raise money. Tickets cost $5 for adults and $3 for students. The student council wants to raise $450.
Write an equation to find the number of each type of ticket they should sell.
Graph the equation
Use your graph to find two different combinations of tickets sold.
Let `x` be the number of adults that buy tickets and `y` the number of students that buy tickets. The problem says that each ticket for an adult costs $5 and each ticket for a student costs $3, and that the total sum wanted to be raised is $450. The corresponding equation to show this is
`5*x +3*y =450`
This is the standard form of equation of a line, in 2D space. If we want to place it in slope-intercept form we need to separate the variables:
`3y =-5x +450` or equivalent
`y = -5/3*x +150`
Thus the slope of the line representing the equation is `m=-5/3` and the `y` intercept (`x=0` ) is `y0 =150` . The graph is below attached. Since negative values of `x` and `y` (number of persons) does not have physical significance, the graph is restricted only to the first quadrant.
From the graph, we se that two pairs `(x,y)` which satisfies the above equation are `(42,80)` and `(60,50)` .
Therefore the sum can be raised selling 42 tickets for adults and 80 tickets for students or alternately selling 60 tickets for adults and 50 tickets for students.
The student council intends to raise $450 in all. They can do this by selling tickets to adults for $5 and to students for $3.
If the number of tickets sold to adults is x, the amount collected is 5x. This leaves 450 - 5x. To collect this the council needs to sell (450 - 5x)/3 tickets to students.
If x represents the number of tickets sold to adults and y is the number of tickets sold to students 5x + 3y = 450
This can be drawn in a graph as follows:
Take any point on the line shown above. If a number of tickets equal to the y coordinate is sold to students and a number equal to the x-coordinate is sold to adults the council will collect $450.