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 one pencil in cents, $n =$ cost of one notebook 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 $16p + 10n = 5.84\ \mathrm{(B)}$ .

2007 AMC 10A (Problems • Answer Key • Resources)
Preceded by Problem 4	Followed by Problem 6
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All AMC 10 Problems and Solutions

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2007 AMC 10A Problems/Problem 5

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