Percentiles and Box Plots · Superchallenge problem

A frequency table groups $N$ scores into classes $0$–$10$: $6$; $10$–$20$: $a$; $20$–$30$: $18$; $30$–$40$: $b$; $40$–$50$: $4$. Quartiles are estimated from the cumulative frequency graph (straight lines between class boundaries, $Q_1$ at cumulative count $N/4$ and $Q_3$ at $3N/4$). The estimates are $Q_1 = 19$ and $Q_3 = 35$. Find $a + b$.