# MOVING COMPANIES

## By: Tina Tsan

Situation: Cost between two moving companies or Moving Company A vs. Moving Company B

The variables are cost and number of hours

Cost: Total amount of money the move will cost depending on the hours. [DEPENDENT VARIABLE]

Number of Hours: The amount of hours it'll take to move [INDEPENDENT VARIABLE]

## Company A

Company A charges customers an upfront cost of \$40 to pay for the move, truck fees, labour cost, etc and \$20 for every hour it takes to move.

Fixed Cost: \$40

Variable Cost [slope]: \$20/hour

m= 20 (slope)

b= 40 (fixed cost)

therefore...

y=mx+b form: y=20x+40

ax+by=c form: 20x-y+40=0

## Company B

Company B charges an upfront cost of only \$20 for the move, truck fees, labour costs, etc but \$50 for every hour it takes to move.

Fixed Cost: \$20

Variable Cost [slope]: \$50/hour

m= 50 (slope)

b= 20 (fixed cost)

therefore...

y=mx+b form: y=50x+20

ax+by=c form: 50x-y+20=0

## click below to see full graph

https://www.desmos.com/calculator/jjqz3u41jf

black line: company A

red line: company B

## INTERSECTION

20x+40=50x+20

20x-50x=20-40

-30x=-20

x=-20/-30

x=0.67

We can now substitute x=0.67 into either equation to find y.

y=20x+40

=20(0.67)+40

=13.4+40

=53.4

Therefore we can conclude that the coordinates of the intersection is (0.67,53.4) OR (64/100, 267/5).

[0.67 hours, \$53.40]

## Significance

The significance of knowing the intersection is that it tells customers at which point the moving companies charge the same amount of money for the same amount of time. This helps tell you that for a move that takes less than 0.67, one company will charge more than the other company and a move that takes longer than 0.67 hours, it's the opposite.

For example, in our case, if you look at the graph above, you can see Company B is cheaper than Company A. But after they intersect, Company A is cheaper than Company B. This means that Company B is cheaper and more ideal for moves that take less than 0.67 hours whereas Company A is more ideal for moves longer than 0.67 hours.

In conclusion, knowing the intersection helps customer determine the best deal for them depending on how long it takes for them to move. [How long it takes to move depends on how much stuff they have]

## Summary Statement

Both company A and company B will charge you \$53.40 for a move that takes 0.67 hours.