# 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?

Result

x =  18 m
y =  6
z =  5

#### Solution:

$a = 3 \cdot \ 10 = 30 \ dm \ \\ b = 3.6 \cdot \ 10 = 36 \ dm \ \\ 30 = 2 \cdot 3 \cdot 5 \\ 36 = 2^2 \cdot 3^2 \\ LCM(30, 36) = 2^2 \cdot 3^2 \cdot 5 = 180\\ \ \\ \ \\ x = LCM(a, b)/10 = LCM(30, 36)/10 = 18 = 18 \ \text{ m }$
$y = 10 \cdot \ x / a = 10 \cdot \ 18 / 30 = 6$
$z = 10 \cdot \ x / b = 10 \cdot \ 18 / 36 = 5$

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