\[\begin{align} \underbrace{\dfrac23 + \dfrac23 + \cdots + \dfrac23}_{\color{green}{A}\color{black} \text{ copies of } \frac23} &= \underbrace{\dfrac45 + \dfrac45 + \cdots + \dfrac45}_{\color{blue}{B}\color{black} \text{ copies of } \frac45} \\\\\\ 20 \leq \color{green}{A}\color{black}+\color{blue}{B}\color{black} &\leq 24\\\\ \color{green}{A}\color{black}+\color{blue}{B}\color{black} &=\, ? \end{align}\]

I have \(\color{green}{A}\color{black}\) copies of \(\frac23\) on the left-hand side of the equality, and \(\color{blue}{B}\color{black}\) copies of \(\frac45\) on the right. In total, I've written down between 20 and 24 fractions. Exactly how many fractions are there?

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