# Bus Company Tour Sales

### By: Phanisri Mudunuri

## Situation

Another bus company called Intercar took a tour bus to Niagara Falls when there were 70 people aboard. The bus charged $360. The next week the bus, had 120 people aboard and charged them $510. If you were suggesting someone to buy a tour bus from one of the companies to Niagara Falls, depending on the number of people. Which company would you choose.

## Table of Values For Magic Tour Bus Company

## Variables

Let y represent the cost

## Magic Tour Bus Equation

Solution:

Let x = the number of people on the bus

Let y = the total cost for the bus with its passengers.

Then, when there are 30 people on the bus (x = 30), the cost was $260 (y = 260). This means the point (x, y) = (30, 260).

Also, when there were 50 people on the bus, the cost was $300. So that is the point (50, 300).

You see - we have two points and so we can write the equation of a line that goes through those points. The first thing we have to do is find the slope.

The slope of the line joining two points is the rise divided by the run. That means

m = (y2 - y1) / (x2 - x1)

So we put in the values of (30, 260) and (50, 300):

m = (300 - 260) / (50 - 30)

m = 40 / 20

m = 2.

The slope is 2. Now we can write it in the form y = mx + b, using 2 for m:

y = 2x + b.

This equation connects both points, so that means it goes through those points. We want to know "b" next, so we can now substitute in either point for the x and the y. I will substitute in x = 50 and y = 220:

300 = 2(50) + b

300 = 100 + b

b + 100 = 300

b = 200.

Now I know the b and the m, so I can finally write the full y=mx + b form of the equation:

y = 2x + 200.

## Magic Tour Bus Graph

## Intercar Tour Bus Table of Values

## Variables

Let y represent the cost

## Intercar Tour Bus Equation

Solution:

Let x = the number of people on the bus

Let y = the total cost for the bus with its passengers aboard.

Then, when there are 70 people on the bus (x = 70), the cost was $360 (y = 360). This means the point (x, y) = (70, 360).

Also, when there were 120 people on the bus, the cost was $510. So that is the point (120, 510).

You see - we have two points and so we can write the equation of a line that goes through those points. The first thing we have to do is find the slope. That means

m = (y2 - y1) / (x2 - x1)

So we put in the values of (70, 360) and (120, 510):

m = (510 - 360) / (120 - 70)

m = 150 / 50

m = 3.

The slope is 3. Now we can write it in the form y = mx + b, using 3 for m:

y = 3x + b.

This equation connects both points, so that means it goes through those points. We want to know "b" next, so we can now substitute in either point for the x and the y. I will substitute in x = 120 and y = 510:

510 = 3(120) + b

510 = 360 + b

b + 360 = 510

b = 150.

Now I know the b and the m, so I can finally write the full y=mx + b form of the equation:

y = 3x + 150.

## Intercar Tour Bus Graph

## Both Graphs and The Intersection Point

## Intersection Point of the Graphs and the solution

*x*when the

*y*values on the two lines are the same. That is, we want to find where the lines intersect, which we can do by solving the system of equations.

For this system, it's easiest to use substitution. Since

* y* = 2x=200,

we have,

y=3x+150

2x+200=3x+150

x=50

We think that if 50 people were aboard, the cost will be the same. Let's check this: if Magic Tour Bus has 50 people aboard, the cost is

2(100)+200 = 300,

and if Intercar has 50 people aboard the cost is,

3(50)+150 = 300.