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:

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

$$\begin{gathered} m_2=100\text{kg} \\ {r}_3=1/r=1/0.8438=\frac{32}{27}\doteq 1.1852 \\ b=r_3\cdot m_2=1.1852\cdot 100=118.5\text{kg} \end{gathered}$$

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