Tailor

From the rest of the cloth, the tailor could cut off either 3 m in men's suits without a vest or 3.6 m with the vest.

What shortest possible length could the rest of the cloth have?

How many suits
a) without a vest
b) With a vest, could you make the tailor from the rest of the fabric wear it?

Correct answer:

x =  18 m
y =  6
z =  5

Step-by-step explanation:

$$\begin{gathered} a=3\cdot 10=30\text{dm} \\ b=3.6\cdot 10=36\text{dm} \\ 30=2\cdot 3\cdot 5 \\ 36=2^2\cdot 3^2 \\ LCM(30,36)=2^2\cdot 3^2\cdot 5=180 \\ x=LCM(a,b)/10=LCM(30,36)/10=18\text{m} \end{gathered}$$

$y=10\cdot x/a=10\cdot 18/30=6$

$z=10\cdot x/b=10\cdot 18/36=5$

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