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2014 AMC 10B Problem 1

Problem 1 of 25EasierAlgebra

Leah has 1313 coins, all of which are pennies and nickels. If she had one more nickel than she has now, then she would have the same number of pennies and nickels. In cents, how much are Leah’s coins worth?

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Solution

Let the number of pennies be p.p. Then, the number of nickels is 13−p13-p and p−1,p-1, so 13−p=p−1.13-p=p-1. This means we have 77 pennies and 66 nickels. Therefore, the number of cents is 7+6⋅5=37.7+6\cdot 5=37. Thus, the correct answer is C .

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Concepts: linear equation · money

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