The school store sells 7 pencils and 8 notebooks for $\mathdollar 4.15$. It also sells 5 pencils and 3 notebooks for $\mathdollar 1.77$. How much do 16 pencils and 10 notebooks cost?
$\text{(A)}\mathdollar 1.76 \qquad \text{(B)}\mathdollar 5.84 \qquad \text{(C)}\mathdollar 6.00 \qquad \text{(D)}\mathdollar 6.16 \qquad \text{(E)}\mathdollar 6.32$
We let $p =$ cost of  one pencil in dollars, $n =$ cost of one notebook in dollars. Then
\begin{align*} 7p + 8n = 4.15 &\Longrightarrow  35p + 40n = 20.75\\ 5p + 3n = 1.77 &\Longrightarrow  35p + 21n = 12.39 \end{align*}
Subtracting these equations yields $19n = 8.36 \Longrightarrow n = 0.44$. Solving backwards gives $p = 0.09$. Thus the answer is $16p + 10n = 5.84\ \mathrm{(B)}$.