AVR - three friends

$2250 is divided among three friends, Ajay, Vijay, and Raj, in such a way that 1/6th of Ajay's share, 1/4th of Vijay's share, and 2/5th of Raj's share is equal. Find Ajay's share.

Final Answer:

A =  1080 USD

Step-by-step explanation:

$$\begin{gathered} x=2250\text{USD} \\ A/6=V/4=2/5R \\ A+V+R=x \\ \frac{A}{6}=\frac{V}{4} \\ \frac{V}{4}=\frac{2}{5}R \\ A+V+R=x \\ A+V+R=2250 \\ A/6=V/4 \\ V/4=2/5\cdot R \\ A+V+R=2250 \\ 2A-3V=0 \\ 8R-5V=0 \\ A+R+V=2250 \\ Row3-\frac{1}{2}\cdot Row1\to Row3 \\ R+2.5V=2250 \\ Row3-\frac{1}{8}\cdot Row2\to Row3 \\ 3.125V=2250 \\ V=\frac{2250}{3.125}=720 \\ R=\frac{0+5V}{8}=\frac{0+5\cdot 720}{8}=450 \\ A=\frac{0+3V}{2}=\frac{0+3\cdot 720}{2}=1080=1080\text{USD} \\ A=1080 \\ R=450 \\ V=720 \end{gathered}$$

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