1B. Lena bought a package of blue and red paper leaves, in which the ratio of the number of blue to the number of red leaves is $2: 7$. Every day, Lena uses 1 blue and 3 red leaves. One day, after taking 3 red leaves and using the last blue leaf in the package, 15 red leaves remained. How many leaves were there in the package at the beginning?
Solution. Let there be $x$ blue and $y$ red leaves in the package at the beginning. Then $\frac{x}{y}=\frac{2}{7}$. Since Lena uses 1 blue and 3 red leaves each day, after $x$ days she has used all the blue leaves and $3x$ red leaves, after which 15 red leaves remained in the package. Therefore, $y=3x+15$. Hence, $\frac{x}{3x+15}=\frac{2}{7}$, from which we get $x=30$. Thus, the package contained 30 blue and $3 \cdot 30+15=105$ red leaves, which means a total of $30+105=135$ leaves.

2AB. If $a$ and $b$ are natural numbers such that $\frac{1}{a}+\frac{1}{2a}+\frac{1}{3a}=\frac{1}{b^2-2b}$, determine the smallest possible value of the sum $a+b$.