Question

An amount of $9000 is divided among four persons A,B,C and D. The sum of shares of A,C and D is four times the share of B. The sum of shares of B and D is equal to four-fifths the sum of shares of A and C. Find the share of D.

Please help!! How to frame equation for share of each person?

Answer 1

just write the data as given:

a+b+c+d = 9000
a+c+d = 4b
b+d = 4/5 (a+c)

The first says that
a+c+d = 9000-b
using the second, that means that
9000-b = 4b
b = 1800

So, now we have
a+c+d = 7200
1800+d = 4/5 (a+c)

Now we know that
a+d = 7200-d, so
1800+d = 4/5 (7200-d)
1800+d = 5760 - 4/5 d
9/5 d = 3960
d = 2200

Answer 2

Thank you very much. Explained neat and wast. I was breaking my head for this.

Answer 3

*neat and good

Answer 4

typing error
this line a+d = 7200-d, so should be,

a+c=7200-d