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Question 1171263: three business partners A, B and C share their profits as follows:
The ratio of A's share to B's share is 6:5 and the ratio of B's share to C's share is 3:4. Determine:
a) A's share, B's share and C's share
b) The total profit if A gets 5000 less than C
Found 2 solutions by Theo, greenestamps:
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! your given ratios are:
A/B = 6/5
B/C = 3/4
from A/B = 6/5, solve for A in terms of B to get A = 6B/5.
from B/C = 3/4, solve for B in terms of C to get B = 3C/4.
from A = 6B/5, solve for B in terms of A to get B = 5A/6.
from B = 3C/4, replace B with 5A/6 to get 5A/6 = 3C/4.
multiply both sides of this equation by 6 to get 5A = 18C/4.
divide both sides of this equation by 5 to get A = 18C/20.
from A = 18C/20, solve for C to get C = 20A/18.
you are given that A = C - 5000.
since C = 20A/18, you get A = 20A/18 - 5000.
multiply both sides of this equation by 18 to get 18A = 20A - 90000.
subtract 18A from both sides of this equation and add 90000 to both sides of this equation to get 90000 = 20A - 18A.
combine like terms to get 90000 = 2A.
solve for A to get A = 90000/2 = 45000
since A = C - 5000, then C = A + 5000 = 45000 + 5000 = 50000.
you have A = 45000 and C = 50000.
since B = 3C/4, then B = 3*50000/4 = 37500.
you now have A = 45000 and B = 37500 and C = 50000.
total profit = A + B + C = 45000 + 37500 + 50000 = 132500, and:
A's share is 45000.
B's share if 37500.
C's share is 50000.
that's your solution.
you were given that A/B = 6/5.
since A = 45000 and B = 37500, then A/B = 45000/37500 = 1.2 * 5/5 = 6/5.
this confirms the ratio is correct with the calculated values of A and B.
you were given that B/C = 3/4.
since B = 37500 and C = 50000, then B/C = 37500/50000 = .75 * 4/4 = 3/4.
this confirms the ratio is correct with the calculated values of B and C.
you were given that A = C - 5000.
since A = 45000 and C = 50000, then you get 45000 = 50000 - 5000 which becomes 45000 = 45000 which it true.
this confirms that A = C - 5000 with the calculated values of A and C.
your solution is confirmed to be good.
the solution is that total profit = 132500 with A = 45000, B = 37500, C = 50000.
Answer by greenestamps(13209)  (Show Source):
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