Tailor

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

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

How many suits
a) without a vest
b) with vest could make the tailor from the rest of the fabric wear?

Correct result:

x =  18 m
y =  6
z =  5

Solution:

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

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

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

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