Johan and Genny are trying to find a moving company

Question

Johan is trying to decide which company he should hire to help him move to his new house. "toss it" company charges a base fee of $120 plus $25 an hour. "crash boom" charges a base fee of $50 plus $40 an hour. Johan thinks he should hire crash boom because the base fee is less. But his girlfriend Genny thinks that they should hire toss it because she thinks it will take a long time to move. Each company rounds up to the nearest whole hour (No partial hour)

 

A) Define variables and write equations to represent the time and total cost of the move

 

B) Initially it cost less to hire crash boom, but eventually toss it is cheaper. What is the smallest number of whole hours after which it is cheaper to hire toss it that crash boom.

 

C) Johan thinks it will take 6 hours to move. Which company should he hire

Answer 1

A)

 

Let x be the amount of time spent moving with the "toss it" company.

 

Let y be the amount of time spent moving with the "crash boom" company.

 

Johan believes the move should take 6 hrs regardless of which company he chooses, so x and y both equal 6. Those are two trivial equations. 

 

x = 6

 

y = 6

 

 

Now the total cost of moving with the "toss it" company is $120 plus $25 for every hour spent moving, which is expressed as 

 

$120 + $25x,

 

and since Johan is only willing to spend 6 hrs to move with either company, x = 6. Therefore, the total cost of moving with "toss it" is 

 

$120 + $25(6) = $120 + $150 = $270.

 

 

 

Now the total cost of moving with "crash boom" is $50 plus $40 for every hour spent moving, which is expressed as

 

$50 + $40y.

 

Again, the time spent moving with either company is the same, so y = 6. Therefore, the total cost of moving with "crash boom" is

 $50 + $40(6) = $50 + $240 = $290.

 

B)

 

    1st hr with "toss it" = $120 + $25(1) = $145.

    1st hr with "crash boom" = $50 + $40(1) = $90

 

    2nd hr with "toss it" =  $120 + $25(2) = $170.

    2nd hr with "crash boom" = $50 + $40(2) = $130

 

    3rd hr with "toss it" = $120 + $25(3) = $195.
    3rd hr with "crash boom" = $50 + $40(3) = $170

 

     4th hr with "toss it" = $120 + $25(4) = $220

     4th hr with "crash boom" = $50 + $40(4) = $210

 

     5th hr with "toss it" = $120 + $25(5) = $245

     5th hr with "crash boom" = $50 + $40(5) = $250

 

 

It is cheaper to hire "toss it" after the 5th hour.

 

 

C)

 

Johan should hire the "toss it" company because it costs $270, as opposed to "crash boom" which costs $290.