Track the students who fail both exams.
\\(\begin{aligned}
\text{Failed first exam} &= 100\% - 70\% = 30\% \text{ of total}
\\
\text{Of those, 80\% pass second} &: 0.30 \times 0.80 = 0.24 = 24\% \text{ of total pass second}
\\
\text{20\% of first-fail fail second} &: 0.30 \times 0.20 = 0.06 = 6\% \text{ fail both}
\\
6\% &\rightarrow 54 \text{ students}
\\
\text{Total students} &= 54 \div 0.06 = 900
\end{aligned}\\)
Final Answer: 900