Question 1126672
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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.<br>
We have
Lob:Love = 17:12  and  Love:Smash = 3:4<br>
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<br>
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.<br>
With all four people now in a single ratio, we can solve the problem.<br>
Lob's share = 34x
Loves' share = 24x
Smash's share = 32x
Vantage's share = 15x<br>
The total earnings were $3150:<br>
{{{34x+24x+32x+15x = 3150}}}
{{{105x = 3150}}}
{{{x = 30}}}<br>
Love's share is 24x = 24*$30 = $720.