Material 3207

How many screws can we make from a rod whose weight is 3 3/4 kg if the weight of the screw is 3/16 kg and we count 3/20 of the material?

Correct answer:

n =  17

Step-by-step explanation:

$$\begin{gathered} m_1=3\frac{3}{4}=3+\frac{3}{4}=\frac{3\cdot 4+3}{4}=\frac{12+3}{4}=\frac{15}{4}=3\frac{3}{4}=3.75\text{kg} \\ {m}_2=\frac{3}{16}=0.1875\text{kg} \\ {m}_3=\frac{3}{20}\cdot m_2=\frac{3}{20}\cdot \frac{3}{16}=\frac{3\cdot 3}{20\cdot 16}=\frac{9}{320}\doteq 0.0281\text{kg} \\ {m}_4=m_2+m_3=\frac{3}{16}+\frac{9}{320}=\frac{60}{320}+\frac{9}{320}=\frac{60+9}{320}=\frac{69}{320}\doteq 0.2156\text{kg} \\ n=\lfloor m_1/m_4\rfloor =\lfloor 3.75/0.2156\rfloor =17 \end{gathered}$$

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