Leftovers 43921

There is less than 50 m of fabric in the package. If we cut only for blouses or only for dresses, we will not have any leftovers. 1.5 m of fabric is used for one blouse and 3.2 m for one dress. Determine the amount of fabric in the package.

Correct answer:

x =  48 m

Step-by-step explanation:

$$\begin{gathered} a=1.5\text{m}\to \text{cm}=1.5\cdot 100\text{cm}=150\text{cm} \\ b=3.2\text{m}\to \text{cm}=3.2\cdot 100\text{cm}=320\text{cm} \\ 150=2\cdot 3\cdot 5^2 \\ 320=2^6\cdot 5 \\ LCM(150,320)=2^6\cdot 3\cdot 5^2=4800 \\ {x}_1=LCM(a,b)=LCM(150,320)=4800\text{cm} \\ x=x_1\to \text{m}=x_1:100\text{m}=4800:100\text{m}=48\text{m} \\ x<50m \end{gathered}$$

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