SOLUTION: The business partners, A, B and C, share the profit as follows: The ratio of A's share to B is 6:5 and the ration of B's share to C is 3:4. Determine: 1.1 A's share: B's share: C

Question 1169673: The business partners, A, B and C, share the profit as follows:
The ratio of A's share to B is 6:5 and the ration of B's share to C 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 math_tutor2020(3816) (Show Source): You can put this solution on YOUR website!

Part (1)

The ratio of A to B is 6:5
The ratio of B to C is 3:4

Let's write the ratios together with arrows connecting them like so
6:5 <--> 3:4

The goal is to get the inner values 5 and 3 to match up and be the same number.

What we can do is multiply both parts of the first ratio by some number x
6:5 turns into 6x:5x

Similarly,
3:4 turns into 3y:4y
for some number y

The LCM of 5 and 3 is 15, so if x = 3 and y = 5, then we get
6x:5x = 6*3:5*3 = 18:15
3y:4y = 3*5:4*5 = 15:20

In short, we found that
6:5 is equivalent to 18:15
3:4 is equivalent to 15:20

Then looking at
18:15 <--> 15:20
we see the inner values are 15 each

We can then link the two new ratios
18:15 <--> 15:20 becomes 18:15:20

Answer = 18:15:20
==============================================

Part (2)

Let m be some positive number

The ratio 18:15:20 means
A's share = 18m
B's share = 15m
C's share = 20m

So basically 18m:15m:20m is equivalent to 18:15:20 if we divide all parts by m.

Person A gets $5000 less compared to C, so,
A = C - 5000
18m = 20m - 5000
18m-20m = -5000
-2m = -5000
m = -5000/(-2)
m = 2500

The total profit is
A+B+C = 18m+15m+20m
A+B+C = 53m
A+B+C = 53*2500
A+B+C = 132,500 dollars

Or you can calculate the individual shares
A = 18m = 18*2500 = 45,000
B = 15m = 15*2500 = 37,500
C = 20m = 20*2500 = 50,000
which adds up to
A+B+C = 45,000+37,500+50,000 = 132,500
which is the same value we got earlier.

Answer = Total profit is 132,500 dollars

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