Two brothers

The two brothers have a total of 48 nuts. Two-thirds of the nuts of the first correspond to 2/5 of the number of nuts of the second. How many nuts does everyone have?

Correct answer:

a =  18
b =  30

Step-by-step explanation:

$$\begin{gathered} a+b=48 \\ 2/3\cdot a=2/5\cdot b \\ a+b=48 \\ 10a-6b=0 \\ Pivot:Row1\leftrightarrow Row2 \\ 10a-6b=0 \\ a+b=48 \\ Row2-\frac{1}{10}\cdot Row1\to Row2 \\ 10a-6b=0 \\ 1.6b=48 \\ b=\frac{48}{1.6}=30 \\ a=\frac{0+6b}{10}=\frac{0+6\cdot 30}{10}=18 \\ a=18 \\ b=30 \end{gathered}$$

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