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.

2014 AMC 12B (Problems • Answer Key • Resources)
Preceded by First Problem	Followed by Problem 2
1 • 2 • 3 • 4 • 5 • 6 • 7 • 8 • 9 • 10 • 11 • 12 • 13 • 14 • 15 • 16 • 17 • 18 • 19 • 20 • 21 • 22 • 23 • 24 • 25
All AMC 12 Problems and Solutions

The problems on this page are copyrighted by the Mathematical Association of America's American Mathematics Competitions.

Page

Toolbox

Search

2014 AMC 12B Problems/Problem 1

Problem

Solution

See also