Each of the 30 boxes in a certain shipment weighs either 10 or 20 pounds, and the average weight of the boxes in the shipment is 18 pounds. If the average weight of the boxes in the shipment is to be reduced to 14 pounds by removing some of the 20-pound boxes, how many 20 pound boxes must be removed?
Assume you have x 10# boxes and y 20# boxes.
x+y = 30
and 10x +20Y = 18*30 = 540
This tells us we have 24 20# boxes and 6 10# boxes.
The easy way to do this at this point would be to backsolve, but since you haven't given me tha answer choices we'll have to do a little math.
we still have 6 10# boxes, but need a new number (z)of 20# boxes, we set it up as follows:
6*10 + 20*Z = 14 (6+Z) That gives us 4 20# boxes remaining. We had to get rid of 20 20# boxes.
Looking at it logically, Since the average is now less than the average of 20# and 10#, there will need to be more 10# boxes than 20# boxes in the shipment.
