Ship boiler age

The ship and boiler are 49 years old. The ship is twice as old as the boiler was when the ship was as old as the boiler is now. How old is the ship?

Final Answer:

L =  28

Step-by-step explanation:

$$\begin{gathered} L+K=49 \\ L=2\cdot (K-x) \\ L-x=K \\ K+L=49 \\ 2K-L-2x=0 \\ K-L+x=0 \\ Pivot:Row1\leftrightarrow Row2 \\ Row2-\frac{1}{2}\cdot Row1\to Row2 \\ 1.5L+x=49 \\ Row3-\frac{1}{2}\cdot Row1\to Row3 \\ -0.5L+2x=0 \\ Row3-\frac{-0.5}{1.5}\cdot Row2\to Row3 \\ 2.333x=16.333 \\ x=\frac{16.33333333}{2.33333333}=7 \\ L=\frac{49-x}{1.5}=\frac{49-7}{1.5}=28 \\ K=\frac{0+L+2x}{2}=\frac{0+28+2\cdot 7}{2}=21 \\ K=21 \\ L=28 \\ x=7 \\ \text{ Verifying Solution: } \\ s=L+K=28+21=49 \\ {l}_7=L-7=28-7=21 \\ {k}_7=K-7=21-7=14 \\ 2\cdot 14=28 \end{gathered}$$

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