A prize of $27,000 is to be divided among three people in the ratio 3:5:7. What is the largest share? This is not homework; I was just reviewing some old math flash cards and I came across this one I couldn't solve. I'm not interested in the solution so much as the reasoning.
Thanks

You can think of splitting the money in the ratio $3:5:7$ as dividing it into $3+5+7=15$ equal parts and giving $3$ of these parts to one person, $5$ to another, and $7$ to the third. One part, then, must amount to $\frac{27000}{15}=1800$ dollars, and the shares must then be $3 \cdot 1800 = 5400$, $5 \cdot 1800 = 9000$, and $7 \cdot 1800 = 12600$ dollars, respectively. (As a quick check, $5400+9000+12600=27000$, as required.)
