Kilograms 69724

The hardware store sold 1 kg of nails for CZK 400 and 1 kg of screws for CZK 800. How many kilograms of nails and how many screws did they sell if they sold a total of 5 kilograms and earned CZK 3,200.

Correct answer:

a =  2 kg
b =  3 kg

Step-by-step explanation:

$$\begin{gathered} m=5\text{kg} \\ a+b=m \\ 400a+800b=3200 \\ a+b=5 \\ 400a+800b=3200 \\ a+b=5 \\ 400\cdot a+800\cdot b=3200 \\ a+b=5 \\ 400a+800b=3200 \\ Pivot:Row1\leftrightarrow Row2 \\ 400a+800b=3200 \\ a+b=5 \\ Row2-\frac{1}{400}\cdot Row1\to Row2 \\ 400a+800b=3200 \\ -b=-3 \\ b=\frac{-3}{-1}=3 \\ a=\frac{3200-800b}{400}=\frac{3200-800\cdot 3}{400}=2=2\text{kg} \\ a=2 \\ b=3 \end{gathered}$$

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