Expert: Steve Holleran - 9/17/2008

Question
One adult and 10 children are in an elevator. If the adult's weight is 4 times the average (arithmetic mean) weight of the children, then the adult's weight is what fraction of the total weight of the 11 people in the elevator?

Answer
Hi Emily,

I would try it this way:

Let W(a) = the adult's weight

   C(t) = the total weight of the 10 children.

Then you have W(a) = 4 * (C(t)/10) or W(a) = .4 * C(t)

Then the fraction comparing the adult's weight to the total of all
the 11 people would be

                    [.4 * C(t)] / [W(a) + C(t)]

or                   [.4 * C(t)] / [.4 * C(t) + C(t)]

                =   [.4 * C(t)] / [ 1.4 * C(t)]

                = .4 / 1.4 = 4/14 = 2/7


That seems to be the easiest to me.

Steve