2014 AMC 12B Problems/Problem 1

Problem

Leah has $13$ 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?

$\textbf{(A)}\ 33\qquad\textbf{(B)}\ 35\qquad\textbf{(C)}\ 37\qquad\textbf{(D)}\ 39\qquad\textbf{(E)}\ 41$

Solution

She has $p$ pennies and $n$ nickels, where $n + p = 13$ . If she had $n+1$ nickels then $n+1 = p$ , so $2n+ 1 = 13$ and $n=6$ . So she has 6 nickels and 7 pennies, which clearly have a value of $\boxed{\textbf{(C)}\ 37}$ cents.

Video Solution 1 (Quick and Easy)

https://youtu.be/rNhg3QxwEO0

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2014 AMC 12B (Problems • Answer Key • Resources)
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All AMC 12 Problems and Solutions

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2014 AMC 12B Problems/Problem 1

Contents

Problem

Solution

Video Solution 1 (Quick and Easy)

See also