Containing 59983

The gardener has to prepare a grass mix containing clover grass and a meadow mixture at a price of CZK 24 per kilogram. A kilogram of mono-grass mixture costs CZK 22, and a kilogram of meadow mixture costs CZK 30. It will determine how many kilograms of meadow mixture and how many clover grass mixtures will be contained in a bag weighing 50 kg.

Correct answer:

a =  37.5 kg
b =  12.5 kg

Step-by-step explanation:

$$\begin{gathered} 24\cdot (a+b)=22\cdot a+30\cdot b \\ a+b=50 \\ 2a-6b=0 \\ a+b=50 \\ Row2-\frac{1}{2}\cdot Row1\to Row2 \\ 2a-6b=0 \\ 4b=50 \\ b=\frac{50}{4}=12.5 \\ a=\frac{0+6b}{2}=\frac{0+6\cdot 12.5}{2}=37.5=37.5\text{kg} \\ a=\frac{75}{2}=37.5 \\ b=\frac{25}{2}=12.5 \end{gathered}$$

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