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

m (Solution)
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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...
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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 \\
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&\Rightarrow 2x=16 \\
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&\Rightarrow x=8 \\
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\end{align*}</cmath>
  
<math>x + 3 + x = 19</math>
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<math>\boxed{\text{B}}</math>
 
 
<math>2x = 16</math>
 
 
 
<math>x = 8</math>
 
 
 
B
 
  
 
==See Also==
 
==See Also==
  
 
[[1986 AJHSME Problems]]
 
[[1986 AJHSME Problems]]

Revision as of 19:22, 24 January 2009

Problem

A picture $3$ feet across is hung in the center of a wall that is $19$ feet wall. 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