Problem:
Danica drove her new car on a trip for a whole number of hours, averaging 55 miles per hour. At the beginning of the trip, miles was displayed on the odometer, where is a 3 -digit number with and . At the end of the trip, the odometer showed miles. What is ?
Answer Choices:
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Solution:
Let be the total mileage of the trip. Then must be a multiple of 55. Also, because , it is a multiple of 9 . Therefore is a multiple of 495 . Because is at most a 3 -digit number and is not equal to . Therefore . Because , the only possible is 106 , so .
OR
Let be the total mileage of the trip. Then must be a multiple of 55 . Also, because is a multiple of 5 . Because and , it follows that and . Therefore , so .
The problems on this page are the property of the MAA's American Mathematics Competitions