Sharing money

A certain sum of money is shared in the ratio 2 :3:9. If the difference between the first and the second is $40, then the amount of money shared is

Correct answer:

x =  560

Step-by-step explanation:

$$\begin{gathered} a:b:c=2:3:9 \\ \mathrm{\mid }a-b\mathrm{\mid }=40 \\ a={\displaystyle \frac{2}{2+3+9}}\cdot x \\ b={\displaystyle \frac{3}{2+3+9}}\cdot x \\ {\displaystyle \frac{2}{2+3+9}}\cdot x-{\displaystyle \frac{3}{2+3+9}}\cdot x=40 \\ x\cdot 2\mathrm{/}(2+3+9)-3\mathrm{/}(2+3+9)\cdot x=40 \\ 0.071429x=-40 \\ {\displaystyle \frac{1}{14}}x=-40 \\ x=-560 \\ x=\mathrm{\mid }x\mathrm{\mid }=\mathrm{\mid }560\mathrm{\mid }=560 \end{gathered}$$

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