2009 AMC 12A Problems/Problem 3
Contents
[hide]Problem
What number is one third of the way from to ?
Solution
Solution 1
We can rewrite the two given fractions as and . (We multiplied all numerators and denominators by .)
Now it is obvious that the interval between them is divided into three parts by the fractions and .
Solution 2
The number we seek can be obtained as a weighted average of the two endpoints, where the closer one has weight and the further one . We compute:
See Also
2009 AMC 12A (Problems • Answer Key • Resources) | |
Preceded by Problem 2 |
Followed by Problem 4 |
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All AMC 12 Problems and Solutions |