Question 1169673
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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

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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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