  A celebrated result of Mantel shows that every graph on $n$ vertices with
$\lfloor n^2/4 \rfloor + 1$ edges must contain a triangle. A robust version of
this result, due to Rademacher, says that there must in fact be at least
$\lfloor n/2 \rfloor$ triangles in any such graph. Another strengthening, due
to the combined efforts of many authors starting with Erd\H{o}s, says that any
such graph must have an edge which is contained in at least $n/6$ triangles.
Following Mubayi, we study the interplay between these two results, that is,
between the number of triangles in such graphs and their book number, the
largest number of triangles sharing an edge. Among other results, Mubayi showed
that for any $1/6 \leq \beta < 1/4$ there is $\gamma > 0$ such that any graph
on $n$ vertices with at least $\lfloor n^2/4\rfloor + 1$ edges and book number
at most $\beta n$ contains at least $(\gamma -o(1))n^3$ triangles. He also
asked for a more precise estimate for $\gamma$ in terms of $\beta$. We make a
conjecture about this dependency and prove this conjecture for $\beta = 1/6$
and for $0.2495 \leq \beta < 1/4$, thereby answering Mubayi's question in these
ranges.
