Four pieces

A 37-centimeter board is cut into four pieces. The first piece and the second piece are the same lengths. Similarly, the third and the fourth piece are the same lengths if the fourth piece is quadruple the difference between the first piece and 10 cm. Find the length of the second piece.

Final Answer:

b =  11 cm

Step-by-step explanation:

$$\begin{gathered} a+b+c+d=37 \\ a=b \\ c=a \\ d=4\cdot (a-10) \\ a+b+c+d=37 \\ a-b=0 \\ a-c=0 \\ 4a-d=40 \\ Pivot:Row1\leftrightarrow Row4 \\ Row2-\frac{1}{4}\cdot Row1\to Row2 \\ -b+0.25d=-10 \\ Row3-\frac{1}{4}\cdot Row1\to Row3 \\ -c+0.25d=-10 \\ Row4-\frac{1}{4}\cdot Row1\to Row4 \\ b+c+1.25d=27 \\ Row4+Row2\to Row4 \\ c+1.5d=17 \\ Row4+Row3\to Row4 \\ 1.75d=7 \\ d=\frac{7}{1.75}=4 \\ c=\frac{-10-0.25d}{-1}=\frac{-10-0.25\cdot 4}{-1}=11 \\ b=\frac{-10-0.25d}{-1}=\frac{-10-0.25\cdot 4}{-1}=11=11\text{cm} \\ a=\frac{40+d}{4}=\frac{40+4}{4}=11 \\ a=11 \\ b=11 \\ c=11 \\ d=4 \end{gathered}$$

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