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 $\frac{5}{9}$ $5/9$ of the whole sum by $50. What was each share?

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Answer 1 · 2016-12-15T05:37:22

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

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

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

and $\frac{5}{9}$ $5/9$ of whole sum is $\frac{5}{9} \times 8 x = \frac{40}{9} x$ $5/9xx8x=40/9x$ .

As A's share exceeds $\frac{40}{9} x$ $40/9x$ by $$ 50$ $$50$ ,

we have $5 x - \frac{40}{9} x = 50$ $5x-40/9x=50$ and multiplying each term by $9$ $9$ , we get

$45 x - 40 x = 50 \times 9$ $45x-40x=50xx9$

or $5 x = 450$ $5x=450$

or $x = \frac{450}{5} = 90$ $x=450/5=90$

Hence A has $90 \times 5 = $ 450$ $90xx5=$450$ and B has $90 \times 3 = $ 270$ $90xx3=$270$ .

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 595/9 of the whole sum by $50. What was each share?