1985 AHSME Problems/Problem 18
Problem
Six bags of marbles contain and marbles, respectively. One bag contains chipped marbles only. The other bags contain no chipped marbles. Jane takes three of the bags and George takes two of the others. Only the bag of chipped marbles remains. If Jane gets twice as many marbles as George, how many chipped marbles are there?
Solution
Let George's bags contain a total of marbles, so Jane's bag contains marbles. This means the total number of non-chipped marbles is , while the total number of marbles is , so the number of chipped marbles must also be congruent to .
The answer choices are congruent modulo 3 to , , , , and respectively, so the only possible number of chipped marbles among these is . Indeed, if Jane takes the bags containing , , and marbles and George takes the remaining bags containing and marbles, then Jane will have a total of marbles, which is twice as many as George's marbles, as desired. Thus the answer is precisely .
See Also
1985 AHSME (Problems • Answer Key • Resources) | ||
Preceded by Problem 17 |
Followed by Problem 19 | |
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