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Question 1169167: 1.Three business partners A, B and C share the 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:
1.1 A's share:B's share:C's share
1.2 The total profit if A gets $5000 less than C
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website!
you are given:
a represents a's share of the profits
b represents b's share of the profits.
c represents c's share of the profits.
a/b = 6/5
b/c = 3/4
from a/b = 6/5, solve for a to get a = 6/5 * b
from b/c = 3/4, solve for c to get c = 4/3 * b
you know that a + b + c = p, where p represents total profit.
replace a and c with their equivalent values in b to get:
6/5 * b + b + 4/3 * b = p
multiply both sides of this equation 15 to get:
18 * b + 15 * b + 20 * b = 15 * p
add them up to get:
53 * b = 15 * p
divide both sides of this equation by 15 to get:
b = 15/53 * p
since a = 6/5 * b, then:
a = 6/5 * 15/53 * p
simplify to get:
a = 18/53 * p
since c = 4/3 * b, then:
c = 4/3 * 15/53 * p
simplify to get:
c = 20/53 * p
add them up to get:
p = a + b + c = 18/53 * p + 15/53 * p + 20/53 * p
your answers for part 1.1 are:
a's share is equal to 18/53 * total profit.
b's share is equal to 15/53 * total profit.
c's share is equal to 20/53 * total profit.
if a gets 5000 less than c, you get:
a = c - 5000
since a = 18/53 * p and c = 20/53 * p, then you get:
18/53 * p = 20/53 * p - 5000
subtract 18/53 * p from both sides of this equation and add 5000 to both sides of this equation to get:
5000 = 2/53 * p
solve for p to get:
p = 5000 * 53/2 = 132500
a's share is 18/53 * 132500 = 45000
b's share is 15/53 * 132500 = 37500
c's share is 20/53 * 132500 = 50000
ratio of a's share to b's share is 45000/37500 = 6/5
ratio of b's share to c's share is 37500 / 50000 = 3/4
requirements of the problem are satisfied.
solution looks good.
solution is:
a's share is 18/53 * 132500 = 45000
b's share is 15/53 * 132500 = 37500
c's share is 20/53 * 132500 = 50000
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