Difference between revisions of "2014 AMC 12B Problems/Problem 1"
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She has <math>p</math> pennies and <math>n</math> nickels, where <math>n + p = 13</math>. If she had <math>n+1</math> nickels then <math>n+1 = p</math>, so <math>2n+ 1 = 13 </math> and <math>n=6</math>. So she has 6 nickels and 7 pennies, which clearly have a value of <math>\boxed{\textbf{(C)}\ 37}</math> cents. | She has <math>p</math> pennies and <math>n</math> nickels, where <math>n + p = 13</math>. If she had <math>n+1</math> nickels then <math>n+1 = p</math>, so <math>2n+ 1 = 13 </math> and <math>n=6</math>. So she has 6 nickels and 7 pennies, which clearly have a value of <math>\boxed{\textbf{(C)}\ 37}</math> cents. | ||
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+ | {{AMC12 box|year=2014|ab=B|before=First Problem|num-a=2}} | ||
+ | {{MAA Notice}} |
Revision as of 13:00, 21 February 2014
Problem
Leah has 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?
$\textbf{(A)}\ 33\qquad\textbf{(B)}\ 35\qquad\textbf{(C)}\ 37\qquad\textbf{(D)}}\ 39\qquad\textbf{(E)}\ 41$ (Error compiling LaTeX. Unknown error_msg)
Solution
She has pennies and
nickels, where
. If she had
nickels then
, so
and
. So she has 6 nickels and 7 pennies, which clearly have a value of
cents.
2014 AMC 12B (Problems • Answer Key • Resources) | |
Preceded by First Problem |
Followed by Problem 2 |
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