SOLUTION: Tennis coaches High Lob and Low Smash decided to share with their assistants (Love and Vantage) the money they earned from tennis lessons. They agreed on the following ratios: Lob

Question 1126672: Tennis coaches High Lob and Low Smash decided to share with their assistants (Love and Vantage) the money they earned from tennis lessons. They agreed on the following ratios: Lob : Love = 17 : 12, Love : Smash = 3: 4, and Smash : Vantage = 32 :15. If their earnings totalled $3,150, how much did Love receive?
Answer by greenestamps(13200) (Show Source): You can put this solution on YOUR website!

For me, the easiest way to solve a problem like this involving multiple ratios is to find ratios equivalent to the given ratios in such a way that the numbers for the same people are the same.

We have
Lob:Love = 17:12 and Love:Smash = 3:4

Change the second ratio to an equivalent ratio where Love's number is the same as in the first ratio. Then we have
Lob:Love = 17:12 and Love:Smash = 12:16
which gives us Lob:Love:Smash = 17:12:16

Now look at Smash:Vantage = 32:15. In the first ratio, Smash's number is 16, which is half of 32. So change the first ratio to an equivalent ratio in which Smash's number is 32.
Lob:Love:Smash = 34:24:32 and Smash:Vantage = 32:15
which gives us Lob:Love:Smash:Vantage = 34:24:32:15.

With all four people now in a single ratio, we can solve the problem.

Lob's share = 34x
Loves' share = 24x
Smash's share = 32x
Vantage's share = 15x

The total earnings were $3150:

Love's share is 24x = 24*$30 = $720.
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