Difference between revisions of "2016 AMC 8 Problems/Problem 14"
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| + | ==Problem== | ||
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Karl's car uses a gallon of gas every <math>35</math> miles, and his gas tank holds <math>14</math> gallons when it is full. One day, Karl started with a full tank of gas, drove <math>350</math> miles, bought <math>8</math> 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? | Karl's car uses a gallon of gas every <math>35</math> miles, and his gas tank holds <math>14</math> gallons when it is full. One day, Karl started with a full tank of gas, drove <math>350</math> miles, bought <math>8</math> 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? | ||
| − | <math>\textbf{(A) | + | <math>\textbf{(A) }525\qquad\textbf{(B) }560\qquad\textbf{(C) }595\qquad\textbf{(D) }665\qquad \textbf{(E) }735</math> |
==Solution== | ==Solution== | ||
| − | Since he uses a gallon of gas every <math>35</math> miles, he had used <math>\frac{350}{35} = 10</math> gallons after <math>350</math> miles. Therefore, after the first leg of his trip he had <math>14 - 10 = 4</math> gallons of gas left. Then, he bought <math>8</math> gallons of gas, which brought him up to <math>12</math> gallons of gas in his gas tank. When he arrived, he had <math>\frac{1}{2} \cdot 14 = 7</math> gallons of gas. So he used <math>5</math> gallons of gas on the second leg of his trip. Therefore, the second part of his trip covered <math>5 \cdot 35 = 175</math> miles. Adding this to the <math>350</math> miles, we see that he drove <math>350 + 175 = \textbf{(A)} 525</math> miles. | + | Since he uses a gallon of gas every <math>35</math> miles, he had used <math>\frac{350}{35} = 10</math> gallons after <math>350</math> miles. Therefore, after the first leg of his trip he had <math>14 - 10 = 4</math> gallons of gas left. Then, he bought <math>8</math> gallons of gas, which brought him up to <math>12</math> gallons of gas in his gas tank. When he arrived, he had <math>\frac{1}{2} \cdot 14 = 7</math> gallons of gas. So he used <math>5</math> gallons of gas on the second leg of his trip. Therefore, the second part of his trip covered <math>5 \cdot 35 = 175</math> miles. Adding this to the <math>350</math> miles, we see that he drove <math>350 + 175 = \boxed{\textbf{(A)} \, 525}</math> miles. |
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| + | ==Video Solution (CREATIVE THINKING!!!)== | ||
| + | https://youtu.be/qLfV9BYVXkI | ||
| + | |||
| + | ~Education, the Study of Everything | ||
| + | |||
| + | ==Video Solution== | ||
| + | https://youtu.be/3keApPoyfMc | ||
| + | |||
| + | ~savannahsolver | ||
| + | ==See Also== | ||
{{AMC8 box|year=2016|num-b=13|num-a=15}} | {{AMC8 box|year=2016|num-b=13|num-a=15}} | ||
{{MAA Notice}} | {{MAA Notice}} | ||
Latest revision as of 01:35, 2 March 2024
Problem
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?
Solution
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.
Video Solution (CREATIVE THINKING!!!)
~Education, the Study of Everything
Video Solution
~savannahsolver
See Also
| 2016 AMC 8 (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 AJHSME/AMC 8 Problems and Solutions | ||
The problems on this page are copyrighted by the Mathematical Association of America's American Mathematics Competitions. 
