2016 AMC 8
Complete problem set with solutions and individual problem pages
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?
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Since he uses a gallon of gas every miles, he had used gallons after miles. Therefore, after the first leg of his trip he had gallons of gas left. Then, he bought gallons of gas, which brought him up to gallons of gas in his gas tank. When he arrived, he had gallons of gas. So he used gallons of gas on the second leg of his trip. Therefore, the second part of his trip covered miles. Adding this to the miles, we see that he drove miles.
