SOLUTION: Divide Rs 12,540 in A B and C so that A may receive 3/7 of B and C, and B receive 2/9 of A and C.

Question 189485: Divide Rs 12,540 in A B and C so that A may receive 3/7 of B and C, and B receive 2/9 of A and C.
Answer by ankor@dixie-net.com(22740) (Show Source): You can put this solution on YOUR website!
Divide Rs 12,540 in A B and C so that A may receive 3/7 of B and C, and B receive 2/9 of A and C.
:
Write an equation for each and arrange in a standard integer form
:
"12,540 in A B and C"
a + b + c = 12540
:
"that A may receive 3/7 of B and C,"
a = (b + c)
multiply both sides by 7
7a = 3(b + c)
7a = 3b + 3c
7a - 3b - 3c = 0
:
" and B receive 2/9 of A and C."
b = (a + c)
multiply both sides by 9
9b = 2(a + c)
9b = 2a + 2c
-2a + 9b - 2c = 0
:
Multiply the 1st equation by 2 and add to the above equation
-2a + 9b - 2c = 0
2a + 2b + 2c = 25080
------------------------adding eliminates a & c, find b
11b = 25080
b =
b = 2280
:
Multiply the 1st equation by 3 and add to the 2nd equation:
3a + 3b + 3c = 37620
7a - 3b - 3c = 0
--------------------addition eliminates b & c, find a
10a = 37620
a =
a = 3762
;
Find c:
3762 + 2280 + c = 12540
c = 12540 - 6042
c = 6498
:
Check solution using a = (b + c)
a = (2280 + 6498)
a = (8778)
a = 3762 as we got above
:
You can check the solutions in the other equations
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