Difference between revisions of "2014 AMC 10B Problems/Problem 14"
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==Problem== | ==Problem== | ||
| + | Danica drove her new car on a trip for a whole number of hours, averaging <math>55</math> miles per hour. At the beginning of the trip, <math>abc</math> miles was displayed on the odometer, where <math>abc</math> is a <math>3</math>-digit number with <math>a\ge1</math> and <math>a+b+c\le7</math>. At the end of the trip, the odometer showed <math>cba</math> miles. What is <math>a^2+b^2+c^2</math>? | ||
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| + | <math> \textbf {(A) } 26 \qquad \textbf {(B) } 27 \qquad \textbf {(C) } 36 \qquad \textbf {(D) } 37 \qquad \textbf {(E) } 41</math> | ||
==Solution== | ==Solution== | ||
Revision as of 13:27, 20 February 2014
Problem
Danica drove her new car on a trip for a whole number of hours, averaging 
miles per hour. At the beginning of the trip, 
miles was displayed on the odometer, where is a 
-digit number with 
and 
. At the end of the trip, the odometer showed 
miles. What is 
?
Solution
See Also
| 2014 AMC 10B (Problems • Answer Key • Resources) | ||
| Preceded by Problem 13 |
Followed by Problem 15 | |
| 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. 
