Difference between revisions of "1986 AJHSME Problems/Problem 10"
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==Problem== | ==Problem== | ||
| − | A picture <math>3</math> feet across is hung in the center of a wall that is <math>19</math> feet | + | A picture <math>3</math> feet across is hung in the center of a wall that is <math>19</math> feet wide. How many feet from the end of the wall is the nearest edge of the picture? |
<math>\text{(A)}\ 1\frac{1}{2} \qquad \text{(B)}\ 8 \qquad \text{(C)}\ 9\frac{1}{2} \qquad \text{(D)}\ 16 \qquad \text{(E)}\ 22</math> | <math>\text{(A)}\ 1\frac{1}{2} \qquad \text{(B)}\ 8 \qquad \text{(C)}\ 9\frac{1}{2} \qquad \text{(D)}\ 16 \qquad \text{(E)}\ 22</math> | ||
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==Solution== | ==Solution== | ||
| − | Let's say that the distance from the picture to the wall is <math>x</math>. Since that distance will be on both sides of the picture (it's in the exact middle), we can say that | + | Let's say that the distance from the picture to the wall is <math>x</math>. Since that distance will be on both sides of the picture (it's in the exact middle), we can say that |
| + | <cmath>\begin{align*} | ||
| + | x + 3 + x = 19 &\Rightarrow 2x+3=19 \\ | ||
| + | &\Rightarrow 2x=16 \\ | ||
| + | &\Rightarrow x=8 \\ | ||
| + | \end{align*}</cmath> | ||
| − | <math> | + | <math>\boxed{\text{B}}</math> |
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==See Also== | ==See Also== | ||
| − | [[ | + | {{AJHSME box|year=1986|num-b=9|num-a=11}} |
| + | [[Category:Introductory Geometry Problems]] | ||
| + | [[Category:Introductory Algebra Problems]] | ||
| + | {{MAA Notice}} | ||
Latest revision as of 18:47, 7 August 2013
Problem
A picture 
feet across is hung in the center of a wall that is 
feet wide. How many feet from the end of the wall is the nearest edge of the picture?
Solution
Let's say that the distance from the picture to the wall is 
. Since that distance will be on both sides of the picture (it's in the exact middle), we can say that
See Also
| 1986 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. 
