# 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...

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.

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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.