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 the number of marbles George has be , and so the number of marbles Jane has is
. Therefore, the total number of non-chipped marbles is
. However, the total number of marbles is
. Therefore, we need a number of chipped marbles
to get a number of non-chipped marbles
.
Since is the only one
, it is the only possible number of chipped marbles,
.
To check, we can see that if Jane takes the and
marble bags and George takes the
and
marble bags, this satisfies the conditions.
See Also
1985 AHSME (Problems • Answer Key • Resources) | ||
Preceded by Problem 17 |
Followed by Problem 19 | |
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