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Difference between revisions of "2022 AMC 8 Problems/Problem 11"

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Henry the donkey has a very long piece of pasta. He takes a number of bites of pasta, each time eating <math>3</math> inches of pasta from the middle of one piece. In the end, he has <math>10</math> pieces of pasta whose total length is <math>17</math> inches. How long, in inches, was the piece of pasta he started with?
 
Henry the donkey has a very long piece of pasta. He takes a number of bites of pasta, each time eating <math>3</math> inches of pasta from the middle of one piece. In the end, he has <math>10</math> pieces of pasta whose total length is <math>17</math> inches. How long, in inches, was the piece of pasta he started with?
  
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<math>\textbf{(A) } 34\qquad\textbf{(B) } 38\qquad\textbf{(C) } 41\qquad\textbf{(D) } 44\qquad\textbf{(E) } 47\qquad</math>
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<math>\textbf{(A) } 34\qquad\textbf{(B) } 38\qquad\textbf{(C) } 41\qquad\textbf{(D) } 44\qquad\textbf{(E) } 47</math>
 +
 
 
==Solution==
 
==Solution==
  
 
If there are <math>10</math> pieces of pasta, Henry took <math>10-1=9</math> bites. Each of these <math>9</math> bites took <math>3</math> inches of pasta out, and thus his bites in total took away <math>9\cdot 3 = 27</math> inches of pasta. Thus, the original piece of pasta was <math>27+17=\boxed{\textbf{(D) } 44}</math> inches long.
 
If there are <math>10</math> pieces of pasta, Henry took <math>10-1=9</math> bites. Each of these <math>9</math> bites took <math>3</math> inches of pasta out, and thus his bites in total took away <math>9\cdot 3 = 27</math> inches of pasta. Thus, the original piece of pasta was <math>27+17=\boxed{\textbf{(D) } 44}</math> inches long.
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 +
~wamofan
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 +
==Video Solution by Math-X (First understand the problem!!!)==
 +
https://youtu.be/oUEa7AjMF2A?si=1Ku2y-sqPm_i3J01&t=1518
 +
 +
~Math-X
 +
 +
==Video Solution (CREATIVE THINKING!!!)==
 +
https://youtu.be/q7bicopSq14
 +
 +
~Education, the Study of Everything
 +
 +
==Video Solution by SpreadTheMathLove==
 +
https://www.youtube.com/watch?v=UmuvflX99ig
 +
 +
==Video Solution==
 +
https://www.youtube.com/watch?v=H1K4WJ93isA
 +
 +
~Mathematical Dexterity
 +
 +
==Video Solution==
 +
https://youtu.be/Ij9pAy6tQSg?t=887
 +
 +
~Interstigation
 +
 +
==Video Solution==
 +
https://youtu.be/p29Fe2dLGs8
 +
 +
~STEMbreezy
 +
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==Video Solution==
 +
https://youtu.be/S6kqa8VUj70
 +
 +
~savannahsolver
  
 
==See Also==  
 
==See Also==  
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{{AMC8 box|year=2022|num-b=9|num-a=11}}
+
{{AMC8 box|year=2022|num-b=10|num-a=12}}
 
{{MAA Notice}}
 
{{MAA Notice}}

Latest revision as of 19:33, 2 September 2024

Problem

Henry the donkey has a very long piece of pasta. He takes a number of bites of pasta, each time eating $3$ inches of pasta from the middle of one piece. In the end, he has $10$ pieces of pasta whose total length is $17$ inches. How long, in inches, was the piece of pasta he started with?

$\textbf{(A) } 34\qquad\textbf{(B) } 38\qquad\textbf{(C) } 41\qquad\textbf{(D) } 44\qquad\textbf{(E) } 47$

Solution

If there are $10$ pieces of pasta, Henry took $10-1=9$ bites. Each of these $9$ bites took $3$ inches of pasta out, and thus his bites in total took away $9\cdot 3 = 27$ inches of pasta. Thus, the original piece of pasta was $27+17=\boxed{\textbf{(D) } 44}$ inches long.

~wamofan

Video Solution by Math-X (First understand the problem!!!)

https://youtu.be/oUEa7AjMF2A?si=1Ku2y-sqPm_i3J01&t=1518

~Math-X

Video Solution (CREATIVE THINKING!!!)

https://youtu.be/q7bicopSq14

~Education, the Study of Everything

Video Solution by SpreadTheMathLove

https://www.youtube.com/watch?v=UmuvflX99ig

Video Solution

https://www.youtube.com/watch?v=H1K4WJ93isA

~Mathematical Dexterity

Video Solution

https://youtu.be/Ij9pAy6tQSg?t=887

~Interstigation

Video Solution

https://youtu.be/p29Fe2dLGs8

~STEMbreezy

Video Solution

https://youtu.be/S6kqa8VUj70

~savannahsolver

See Also

2022 AMC 8 (Problems • Answer Key • Resources)
Preceded by
Problem 10 		Followed by
Problem 12
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 AJHSME/AMC 8 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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