Number ratio

Images of three numbers are marked on the number line: 0, m, 3 m-1. The marked pieces are the same length.

a) express the ratio m:(3 m-1)
b) mark and describe the image of the number 1 on the number line.

Final Answer:

r =  0.625
x =  0.1429

Step-by-step explanation:

$$\begin{gathered} m=5\cdot x \\ 3\cdot m-1=8\cdot x \\ m-5x=0 \\ 3m-8x=1 \\ Pivot:Row1\leftrightarrow Row2 \\ Row2-\frac{1}{3}\cdot Row1\to Row2 \\ -2.33x=-0.33 \\ x=\frac{-0.33333333}{-2.33333333}=0.14285714 \\ m=\frac{1+8x}{3}=\frac{1+8\cdot 0.14285714}{3}=0.71428571 \\ m=\frac{5}{7}\doteq 0.714286 \\ x=\frac{1}{7}\doteq 0.142857 \\ r=m/(3\cdot m-1)=0.7143/(3\cdot 0.7143-1)=\frac{5}{8}=0.625 \end{gathered}$$

$x=0.1429=\frac{1}{7}$

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