Production 81205

How many figurines can a potter make from 133 1/3 kg of clay if he needs 4/15 kg of clay to make one and 1/20 of the material is wasted during production?

Correct answer:

n =  475

Step-by-step explanation:

$$\begin{gathered} m=133\frac{1}{3}=133+\frac{1}{3}=\frac{133\cdot 3+1}{3}=\frac{399+1}{3}=\frac{400}{3}=133\frac{1}{3}\doteq 133.3333\text{kg} \\ r=1/20=\frac{1}{20}=0.05 \\ k=1-r=1-\frac{1}{20}=\frac{1\cdot 20}{20}-\frac{1}{20}=\frac{20}{20}-\frac{1}{20}=\frac{20-1}{20}=\frac{19}{20}=0.95 \\ {m}_1=k\cdot m=\frac{19}{20}\cdot \frac{400}{3}=\frac{19\cdot 400}{20\cdot 3}=\frac{7600}{60}=\frac{380}{3}=126\frac{2}{3}\doteq 126.6667\text{kg} \\ {m}_2=\frac{4}{15}\doteq 0.2667\text{kg} \\ n=m_1/m_2=\frac{380}{3}/\frac{4}{15}=\frac{380}{3}:\frac{4}{15}=\frac{380}{3}\cdot \frac{15}{4}=\frac{380\cdot 15}{3\cdot 4}=\frac{5700}{12}=475 \end{gathered}$$

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