Easy math I can't figure out.

Question

The freight elevator of a building can safely carry a load of at most 4000 lb. A worker needs to move supplies in 50-lb boxes from the loading dock to the fourth floor of the building. The worker weighs 160 lb. The cart she uses weighs 95 lb.

 

a. What is the greatest numbe rof boxes she can move in one trip?

 

 

b. The worker must deliver 310 boxes to the fourth floor. How many trips must she make?

Answer 1

The worker plus the cart together weigh 160 lb. + 95 lb. = 255 lb.

 

Since the weight in the elevator cannot exceed 4000 lb., in order to

carry boxes + cart + worker the boxes cannot exceed a weight of

4000 - 255 = 3745 lb.

 

1.  The weight of the boxes must be less than or equal to 3745 lb

     and each box weighs 50 lb.  Let b = # boxes.

     50b ≤ 3745. 

       b ≤ 3745/50

       b ≤ 74.9

Since we cannot take .9 boxes, the most boxes the worker can take in one trip is 74.

If we add a 75th box the total weight will be greater than 4000 pounds.

 

Note:  74*50 + 255 = 3955 lb.

          75*50 + 255 = 4005 lb.

 

2.  We can take 74 boxes per trip and we have 310 boxes.

     (#boxes)/(#boxes/trip) = trip  so  divide 310/74

     310/74 = 4.189  or  4.2 trips

     This actually means we will require 5 trips total

     4 trips will be made with 74 boxes (74*4 = 296 boxes)

     The 5th trip will include the last 14 boxes.

 

Hope this helps.