$15 plus $5.50 per hour to mow lawns. arie char $12 plus 6.25 per hour to mow lawns. in what situations is aries charge greater than or equal to davids charge?

Question

David charges $15 plus $5.50 per hour to mow lawns. Ari charges $12 plus $6.25 per hour to mow lawns. In qhat situations is aries charge greater than or equal to davids charge?

Answer 1

Hi Bianca,

 

Let's begin by seeing whose charge is greater for a 1 hour mowing job:

    David's mowing charge:  $15 + $5.50(1) = $20.50

    Ari's mowing charge:  $12 + 6.25(1) = $18.25

 

We can see that initially, David's mowing charge will be greater than Ari's mowing charge.

 

To find out how big a mowing job (in hours) it will take for Ari's mowing charge to equal David's mowing charge, we can set up expressions in terms of x hours to represent each of their mowing charges.  Then we will set them equal to each other and solve for x (number of hours it takes for them to charge the same amount):

    David's mowing charge:  15 + 5.50x

    Ari's mowing charge:  12 + 6.25x

    15 + 5.50x = 12 + 6.25x (equal mowing charges)

    6.25x - 5.50x = 15 - 12

               0.75x = 3

                     x = 3 / 0.75

                     x = 4 hours (equal mowing charges)

                     x > 4 hours (Ari charges more)

 

So we see it will take at least a 4 hour mowing job for Ari's mowing charge to catch up with David's mowing charge and that a mowing job greater than 4 hours will have Ari's mowing charge surpass David's.

 

Thanks for submitting this problem and glad to help.

 

God bless, Jordan.