Share money

Three Friends shared an amount in the ratio of 2/3 : 3/5: 1/4. Suppose the largest share was Le 12,000.00. How much was shared between them?

Final Answer:

x =  273000

Step-by-step explanation:

$$\begin{gathered} d_1=\frac{2}{3}\doteq 0.6667 \\ {d}_2=\frac{3}{5}=0.6 \\ {d}_3=\frac{1}{4}=0.25 \\ {d}_1:d_2:d_3 \\ {d}_1>d_2>d_3 \\ a=120000 \\ a=d_1\frac{d_1+d_2}{d_3}\cdot x \\ x=\frac{d_1+d_2+d_3}{d_1}\cdot a=\frac{\frac{2}{3}+\frac{3}{5}+\frac{1}{4}}{\frac{2}{3}}\cdot 120000=273000 \\ \text{ Verifying Solution: } \\ b=\frac{d_2}{d_1+d_2+d_3}\cdot x=\frac{\frac{3}{5}}{\frac{2}{3}+\frac{3}{5}+\frac{1}{4}}\cdot 273000=108000 \\ c=\frac{d_3}{d_1+d_2+d_3}\cdot x=\frac{\frac{1}{4}}{\frac{2}{3}+\frac{3}{5}+\frac{1}{4}}\cdot 273000=45000 \end{gathered}$$

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