Mushrooms

The ratio of dry matter and water is 1:9 for most mushrooms. Dry matter consists of carbohydrates, proteins, minerals, fat, and water in a ratio of 50:30:8:3:9. How many kilograms of fresh mushrooms need to be processed into a 10 kg package of dried mushrooms? What is the weight of the individual dry matter components in this package?

Final Answer:

a =  100 kg
s₁ =  5 kg
s₂ =  3 kg
s₃ =  0.8 kg
s₄ =  0.3 kg
s₅ =  0.9 kg

Step-by-step explanation:

$$\begin{gathered} s=10\text{kg} \\ s:w=1:9 \\ w=9\cdot s=9\cdot 10=90\text{kg} \\ a=s+w=10+90=100\text{kg} \end{gathered}$$

$$\begin{gathered} d=50+30+8+3+9=100 \\ {s}_1=\frac{50}{d}\cdot s=\frac{50}{100}\cdot 10=\frac{50\cdot 10}{100}=\frac{500}{100}=5\text{kg} \end{gathered}$$

$s_2=\frac{30}{d}\cdot s=\frac{30}{100}\cdot 10=\frac{30\cdot 10}{100}=\frac{300}{100}=3\text{kg}$

$s_3=\frac{8}{d}\cdot s=\frac{8}{100}\cdot 10=\frac{8\cdot 10}{100}=\frac{80}{100}=\frac{4}{5}\text{kg}=0.8\text{kg}$

$s_4=\frac{3}{d}\cdot s=\frac{3}{100}\cdot 10=\frac{3\cdot 10}{100}=\frac{30}{100}=\frac{3}{10}\text{kg}=0.3\text{kg}$

$s_5=\frac{9}{d}\cdot s=\frac{9}{100}\cdot 10=\frac{9\cdot 10}{100}=\frac{90}{100}=\frac{9}{10}\text{kg}=0.9\text{kg}$

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