# Difference between revisions of "2007 AMC 10A Problems/Problem 5"

## Problem

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?

$\text{(A)}\mathdollar 1.76 \qquad \text{(B)}\mathdollar 5.84 \qquad \text{(C)}\mathdollar 6.00 \qquad \text{(D)}\mathdollar 6.16 \qquad \text{(E)}\mathdollar 6.32$

## Solution

We let $p =$ cost of pencils in cents, $n =$ number of notebooks in cents. 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 $19n = 8.36 \Longrightarrow n = .44$. Backwards solving gives $p = .09$. Thus the answer is $16p + 10n = 5.84\ \mathrm{(B)}$.