Difference between revisions of "2009 AMC 12A Problems/Problem 3"
(New page: == Problem == What number is one third of the way from <math>\frac14</math> to <math>\frac34</math>? <math>\textbf{(A)}\ \frac {1}{3} \qquad \textbf{(B)}\ \frac {5}{12} \qquad \textbf{(C)...) |
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Latest revision as of 21:41, 3 July 2013
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 |
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 AMC 12 Problems and Solutions |
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