Strudel piece length

Mom divided the strudel among her three sons. First, she cut off 1/3 of the strudel. She split the rest in a ratio of 2:3. The difference between the longest and shortest pieces is 4 cm. Determine the length of the strudel in cm.

Final Answer:

x =  30 cm

Step-by-step explanation:

$$\begin{gathered} a+b+c=x \\ a=x/3 \\ b+c=2/3\cdot x \\ b:c=2:3 \\ 3b=2c \\ c-b=4 \\ 3\cdot b=2\cdot c \\ c-b=4 \\ 3b-2c=0 \\ b-c=-4 \\ Row2-\frac{1}{3}\cdot Row1\to Row2 \\ -0.33c=-4 \\ c=\frac{-4}{-0.33333333}=12 \\ b=\frac{0+2c}{3}=\frac{0+2\cdot 12}{3}=8 \\ b=8 \\ c=12 \\ x=\frac{3}{2}\cdot (b+c)=\frac{3}{2}\cdot (8+12)=30=30\text{cm} \\ \text{ Verifying Solution: } \\ a=x/3=30/3=10\text{cm} \\ b=8\text{cm} \\ c=12\text{cm} \\ X=a+b+c=10+8+12=30\text{cm} \end{gathered}$$

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