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Difference between revisions of "2014 AMC 10B Problems/Problem 1"

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==Solution==
 
==Solution==
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If Leah has <math>1</math> more nickel, she has <math>14</math> total coins. Because she has the same number of nickels and pennies, she has <math>7</math> nickels and <math>7</math> pennies. This is after the nickel has been added, so we must subtract <math>1</math> nickel to get <math>6</math> nickels and <math>7</math> pennies. Therefore, Leah has <math>6\cdot5+7=\boxed{37 (\textbf{C})}</math> cents.
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==Video Solution (CREATIVE THINKING)==
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https://youtu.be/0IBJKYzefMU
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~Education, the Study of Everything
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==Video Solution==
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https://youtu.be/vcODyV5g8IQ
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~savannahsolver
  
 
==See Also==
 
==See Also==
 
{{AMC10 box|year=2014|ab=B|before=First Problem|num-a=2}}
 
{{AMC10 box|year=2014|ab=B|before=First Problem|num-a=2}}
 
{{MAA Notice}}
 
{{MAA Notice}}

Latest revision as of 11:06, 2 July 2023

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

~Education, the Study of Everything


Video Solution

https://youtu.be/vcODyV5g8IQ

~savannahsolver

See Also

2014 AMC 10B (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 10 Problems and Solutions

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

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