Find the percentage who failed both exams, then work back to the total.<br><br>\\(\begin{aligned}<br>\text{Failed first exam} &= 35\% \text{ of total}<br>\\<br>\text{Of those, 80\% pass retest} &: 0.35 \times 0.80 = 0.28 = 28\% \text{ pass retest}<br>\\<br>\text{20\% of first-fail fail retest} &: 0.35 \times 0.20 = 0.07 = 7\% \text{ fail both}<br>\\<br>\text{Overall pass} &= 65\% + 28\% = 93\% \; \checkmark<br>\\<br>7\% &\rightarrow 28 \text{ students}<br>\\<br>\text{Total} &= 28 \div 0.07 = 400<br>\end{aligned}\\)<br><br>Final Answer: 400