2014 AMC 10B 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

If Leah has $1$ more nickel, she has $14$ total coins. Because she has the same number of nickels and pennies, she has $7$ nickels and $7$ pennies. This is after the nickel has been added, so we must subtract $1$ nickel to get $6$ nickels and $7$ pennies. Therefore, Leah has $6\cdot5+7=\boxed{37 (\textbf{C})}$ cents.

Video Solution (CREATIVE THINKING)

https://youtu.be/0IBJKYzefMU

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Video Solution

https://youtu.be/vcODyV5g8IQ

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See Also

2014 AMC 10B (ProblemsAnswer KeyResources)
Preceded by
First Problem
Followed by
Problem 2
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All AMC 10 Problems and Solutions

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