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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? | ||
| − | <math>\textbf{(A) } 34\qquad\textbf{(B) } 38\qquad\textbf{(C) } 41\qquad\textbf{(D) } 44\qquad\textbf{(E) } 47 | + | <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. | ||
| + | ~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== | ==See Also== | ||
{{AMC8 box|year=2022|num-b=10|num-a=12}} | {{AMC8 box|year=2022|num-b=10|num-a=12}} | ||
{{MAA Notice}} | {{MAA Notice}} | ||
Latest revision as of 19:33, 2 September 2024
Contents
Problem
Henry the donkey has a very long piece of pasta. He takes a number of bites of pasta, each time eating 
inches of pasta from the middle of one piece. In the end, he has 
pieces of pasta whose total length is 
inches. How long, in inches, was the piece of pasta he started with?
Solution
If there are pieces of pasta, Henry took 
bites. Each of these 
bites took inches of pasta out, and thus his bites in total took away 
inches of pasta. Thus, the original piece of pasta was 
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!!!)
~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
~STEMbreezy
Video Solution
~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 | ||
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