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Difference between revisions of "1986 AJHSME Problems/Problem 10"

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==Problem==
 
==Problem==
  
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A picture <math>3</math> feet across is hung in the center of a wall that is <math>19</math> feet Tall.  How many feet from the end of the wall is the nearest edge of the picture?
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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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[[Category:Introductory Geometry Problems]]
 
[[Category:Introductory Geometry Problems]]
 
[[Category:Introductory Algebra Problems]]
 
[[Category:Introductory Algebra Problems]]
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{{MAA Notice}}

Latest revision as of 17:47, 7 August 2013

Problem

A picture $3$ feet across is hung in the center of a wall that is $19$ feet wide. How many feet from the end of the wall is the nearest edge of the picture?

$\text{(A)}\ 1\frac{1}{2} \qquad \text{(B)}\ 8 \qquad \text{(C)}\ 9\frac{1}{2} \qquad \text{(D)}\ 16 \qquad \text{(E)}\ 22$

Solution

Let's say that the distance from the picture to the wall is $x$. Since that distance will be on both sides of the picture (it's in the exact middle), we can say that \begin{align*} x + 3 + x = 19 &\Rightarrow 2x+3=19 \\ &\Rightarrow 2x=16 \\ &\Rightarrow x=8 \\ \end{align*}

$\boxed{\text{B}}$

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

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