Baking bread

When grinding 100 kg of grain, we obtain 75 kg of flour for food purposes, about 23 kg of bran, which has further use, and about 2 kg is waste. 4.5 kg of bread is baked from 4 kg of flour.

a) Baker can bake how many kilograms of bread from 100 kg grain?
b) How many kilograms of grain is needed per 100 kg of bread?

Correct answer:

a =  84.4 kg
b =  118.5 kg

Step-by-step explanation:

$$\begin{gathered} r_1=\frac{75}{100}=\frac{3}{4}=0.75 \\ {r}_2=\frac{4.5}{4}=\frac{9}{8}=1.125 \\ r=r_1\cdot r_2=\frac{3}{4}\cdot \frac{9}{8}=\frac{3\cdot 9}{4\cdot 8}=\frac{27}{32}\doteq 0.8438 \\ {m}_1=100\text{kg} \\ a=m_1\cdot r=100\cdot \frac{27}{32}=\frac{100\cdot 27}{32}=\frac{2700}{32}=\frac{675}{8}\text{kg}=84.4\text{kg} \end{gathered}$$

$$\begin{gathered} m_2=100\text{kg} \\ {r}_3=1/r=1/\frac{27}{32}=1:\frac{27}{32}=1\cdot \frac{32}{27}=\frac{1\cdot 32}{27}=\frac{32}{27}\doteq 1.1852 \\ b=r_3\cdot m_2=\frac{32}{27}\cdot 100=\frac{32\cdot 100}{27}=\frac{3200}{27}=\frac{3200}{27}\text{kg}=118.5\text{kg} \end{gathered}$$

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