2016 AMC 8 Problem 14
Attempt Problem 14 of the 2016 AMC 8 below, then check your answer against the video solution and professionally curated solution from LIVE by Po-Shen Loh. You can also try the full timed exam, view all 2016 AMC 8 solutions, or check the answer key.
All problems are used with official legal permission of the Mathematical Association of America (MAA).
14.
Karl’s car uses a gallon of gas every miles, and his gas tank holds gallons when it is full.
One day, Karl started with a full tank of gas, drove miles, bought gallons of gas, and continued driving to his destination. When he arrived, his gas tank was half full. How many miles did Karl drive that day?
Answer: A
Small hint:
Track gallons of gas rather than miles at first.
Big hint:
After the -mile drive and the refill, compare the new amount of gas to half a tank.
Video solution:
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Written solution:
If Karl drove miles, then he used gallons of gas.
When he bought more gas, he added gallons to gallons, attaining a total of gallons.
If his tank was half full when he arrived, he used gallons, which equates to miles.
Therefore, he traveled a total distance of miles.
Thus, A is the correct answer.
Problem 14 in other years
- 1985 AMC 8
- 1986 AMC 8
- 1987 AMC 8
- 1988 AMC 8
- 1989 AMC 8
- 1990 AMC 8
- 1991 AMC 8
- 1992 AMC 8
- 1993 AMC 8
- 1994 AMC 8
- 1995 AMC 8
- 1996 AMC 8
- 1997 AMC 8
- 1998 AMC 8
- 1999 AMC 8
- 2000 AMC 8
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