2007 AMC 10A Problems/Problem 5

Problem

A school store sells 7 pencils and 8 notebooks for $$$ 4.15 $. It also sells 5 pencils and 3 notebooks for$ $ $1.77$ . How much do 16 pencils and 10 notebooks cost?

$\text{(A)}\ $$ 1.76 \qquad \text{(B)}\ $ $5.84 \qquad \text{(C)}\ $$ 6.00 \qquad \text{(D)}\ $ $6.16 \qquad \text{(E)}\ $$ 6.32 $== Solution == We let$ p = $cost of pencils in cents,$ n = $number of notebooks in cents. Then

<cmath>\begin{align*} 7p + 8n = 415 &\Longrightarrow 35p + 40n = 2075\\ 5p + 3n = 177 &\Longrightarrow 35p + 21n = 1239 \end{align*}</cmath>

Subtracting these equations yields$ (Error compiling LaTeX. Unknown error_msg)19n = 836 \Longrightarrow n = 44 $. Backwards solving gives$ p = 9 $. Thus the answer is$ 16p + 10n = 584\ \mathrm{(B)}$.

2007 AMC 10A (Problems • Answer Key • Resources)
Preceded by Problem 4	Followed by Problem 6
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2007 AMC 10A Problems/Problem 5

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