Difference between revisions of "1997 AJHSME Problems/Problem 10"
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Latest revision as of 23:26, 4 July 2013
Contents
Problem 10
What fraction of this square region is shaded? Stripes are equal in width, and the figure is drawn to scale.
![[asy] unitsize(8); fill((0,0)--(6,0)--(6,6)--(0,6)--cycle,black); fill((0,0)--(5,0)--(5,5)--(0,5)--cycle,white); fill((0,0)--(4,0)--(4,4)--(0,4)--cycle,black); fill((0,0)--(3,0)--(3,3)--(0,3)--cycle,white); fill((0,0)--(2,0)--(2,2)--(0,2)--cycle,black); fill((0,0)--(1,0)--(1,1)--(0,1)--cycle,white); draw((0,6)--(0,0)--(6,0)); [/asy]](http://latex.artofproblemsolving.com/b/8/6/b86c93e913025a304bc6292d9f589f70d95dda2e.png)
Solution 1
Fill in grid lines to make the shape look like a small 6x6 checkerboard.
There are 
squares total. The smallest shaded region has 
squares. The medium shaded region has 
squares. The largest shaded region has 
squares. The total shaded area is 
squares.
Thus, 
of the square is shaded, and the answer is 
Solution 2
Similar to the first solution, fill in the gridlines to make 
squares total.
Instead of counting shaded squares, count unshaded squares. There are 
unshaded squares.
Thus 
of the square is unshaded, and 
of the square is shaded.
See also
| 1997 AJHSME (Problems • Answer Key • Resources) | ||
| Preceded by Problem 9 |
Followed by Problem 11 | |
| 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 AJHSME/AMC 8 Problems and Solutions | ||
The problems on this page are copyrighted by the Mathematical Association of America's American Mathematics Competitions. 
