A sum

A sum of money is shared between Peter, John, and Henry in the ratio 2:3:5.
a) express Henry's share as a fraction of John's share.
b) what fraction of the whole sum of money is John's share?

Correct answer:

a =  1.6667
J =  0.3

Step-by-step explanation:

$$\begin{gathered} P:J:H=2:3:5 \\ P=\frac{2}{2+3+5}=\frac{1}{5}=0.2 \\ J=\frac{3}{2+3+5}=\frac{3}{10}=0.3 \\ H=\frac{5}{2+3+5}=\frac{1}{2}=0.5 \\ a=H/J=\frac{1}{2}/\frac{3}{10}=\frac{1}{2}:\frac{3}{10}=\frac{1}{2}\cdot \frac{10}{3}=\frac{1\cdot 10}{2\cdot 3}=\frac{10}{6}=\frac{5}{3}=1\frac{2}{3}=1.6667 \end{gathered}$$

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