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? | ||
| − | <math>\textbf{(A)} | + | <math>\textbf{(A) } 34\qquad\textbf{(B) } 38\qquad\textbf{(C) } 41\qquad\textbf{(D) } 44\qquad\textbf{(E) } 47\qquad</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{\qquad\textbf{(D) } 44}</math> inches long. | ||
==See Also== | ==See Also== | ||
{{AMC8 box|year=2022|num-b=9|num-a=11}} | {{AMC8 box|year=2022|num-b=9|num-a=11}} | ||
{{MAA Notice}} | {{MAA Notice}} | ||
Revision as of 11:07, 28 January 2022
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.
See Also
| 2022 AMC 8 (Problems • Answer Key • Resources) | ||
| Preceded by Problem 9 |
Followed by Problem 11 | |
| 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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