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2007 AMC 10A Problem 5

Problem 5 of 25EasierAlgebra

A school store sells 77 pencils and 88 notebooks for $4.15.\$4.15. It also sells 55 pencils and 33 notebooks for $1.77.\$1.77. How much do 1616 pencils and 1010 notebooks cost?

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Solution

Let pp and nn be the prices in cents of a pencil and a notebook. Then 7p+8n=415 7p + 8n = 415 5p+3n=177. 5p + 3n = 177. Solving this system gives p=9p = 9 and n=44.n = 44. So 1616 pencils and 1010 notebooks cost 16(9)+10(44)=58416(9) + 10(44) = 584 cents, or $5.84.\$5.84. Thus, the correct answer is B.

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Concepts: system of equations · money

Problem text and solution from the LIVE past-contest archive. See also the AoPS wiki page for community solutions.