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
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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):
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.
