Finding other point's values on a line knowing one point and distance between two others

Question

So I have a normal line that has points $A, B, C$ and $D$ on it (same order). The distance between $A$ and $D$ is $392$. Point $B$ is equal to $293$. $$CD = 2AB = 4BC$$

Picture of the problem (drawn with my excellent paint skills): How could I find values of these points?

Thanks in advance!

Answer 1

Let $\overline{BC}=x$, then you have $$\overline{AD} = \overline{AB}+\overline{BC}+\overline{CD} = 2x+x+4x=392$$ so by solving for $x$ you get $x = \frac{392}{7} = 56$. Then consequently $$\begin{cases} \overline{AB} = 2 \cdot x = 2 \cdot 56 = 112\\ \overline{BC} = x = 56\\ \overline{CD} = 4 \cdot x = 2 \cdot 56 = 224\\ \end{cases}$$ hence $$\begin{cases} A = D - 392 = 573 - 392 = 181\\ B = 293\\ C = B + \overline{BC} = 293 + 56 = 349\\ D = B + \overline{BC} + \overline{CD} = 293 + 56 + 224 = 573 \end{cases}$$