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 20:41, 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:
![\[\dfrac{ 2\cdot\frac 14 + 1\cdot\frac 34 }3 = \dfrac{ \frac 54 }3 = \boxed{\dfrac 5{12}}\]](http://latex.artofproblemsolving.com/e/9/d/e9df9a575080cb97e25bff7b8f04b8350ef290d5.png)
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 | |
The problems on this page are copyrighted by the Mathematical Association of America's American Mathematics Competitions. 
