The tailor

The tailor estimated the rest of the fabric in the package at 11 m. By measuring, he found that he could cut the same pieces of this fabric without a residue in 150 cm or 210 cm increments. How many meters of fabric were in the package?

Correct answer:

x =  10.5 m

Step-by-step explanation:

$$\begin{gathered} x\doteq 11m=1100cm \\ 150=2\cdot 3\cdot 5^2 \\ 210=2\cdot 3\cdot 5\cdot 7 \\ LCM(150,210)=2\cdot 3\cdot 5^2\cdot 7=1050 \\ n=LCM(150,210)=1050\text{cm} \\ n\doteq 1100cm \\ x=n\to \text{m}=n:100\text{m}=1050:100\text{m}=10.5\text{m}=10.5\text{m} \end{gathered}$$

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