A sum of money was divided between A and B so that A's share was to B's share as 5 is to 3. Also, A's share exceeded #5/9# of the whole sum by $50. What was each share?

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Answer 1 · 2016-12-15T05:37:22

A has #$450# and B has #$270#

Let A's share be #5x# and B's share be #3x#.

As such the whole sum of money is #5x+3x=8x#

and #5/9# of whole sum is #5/9xx8x=40/9x#.

As A's share exceeds #40/9x# by #$50#,

we have #5x-40/9x=50# and multiplying each term by #9#, we get

#45x-40x=50xx9#

or #5x=450#

or #x=450/5=90#

Hence A has #90xx5=$450# and B has #90xx3=$270#.