Question
A sum of money is divided among three brothers in the ratio 5:6:8. If the difference between the amounts received by the youngest and oldest brothers is $200, find the total amount.
A sum of money is divided among three brothers in the ratio 5:6:8. If the difference between the amounts received by the youngest and oldest brothers is $200, find the total amount.
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Koala Tutor
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Let the common ratio be $r$. The youngest brother receives $5r$ dollars, and the oldest brother receives $8r$ dollars. The difference between the amounts received by the youngest and oldest brothers is $8r-5r=3r=200$, so $r=200/3=66.\overline{6}$. The total amount of money divided among the three brothers is $(5r+6r+8r)=19r=3(3r)+10r=3\cdot 200+10\cdot\frac{200}{3}=600+666.\overline{6}=\boxed{1266.\overline{6}}$ dollars.
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