Difference between revisions of "1968 AHSME Problems/Problem 24"

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== Solution ==
 
== Solution ==
<math>\fbox{C}</math>
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Let the width of the frame on the sides to be <math>x</math>.
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Then, the width of the frame on the top and bottom is <math>2x</math>.
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The area of the frame is then <math>x\cdot 2x-18\cdot24</math>
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Setting the area of the frame equal to the area of the picture,
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<cmath>x\cdot 2x-18\cdot24 = 18\cdot24</cmath>
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<cmath>x^2 = 18\cdot24</cmath>
  
 
== See also ==
 
== See also ==

Revision as of 11:07, 10 March 2020

Problem

A painting $18$" X $24$" is to be placed into a wooden frame with the longer dimension vertical. The wood at the top and bottom is twice as wide as the wood on the sides. If the frame area equals that of the painting itself, the ratio of the smaller to the larger dimension of the framed painting is:

$\text{(A) } 1:3\quad \text{(B) } 1:2\quad \text{(C) } 2:3\quad \text{(D) } 3:4\quad \text{(E) } 1:1$


Solution

Let the width of the frame on the sides to be $x$.

Then, the width of the frame on the top and bottom is $2x$.

The area of the frame is then $x\cdot 2x-18\cdot24$

Setting the area of the frame equal to the area of the picture, \[x\cdot 2x-18\cdot24 = 18\cdot24\] \[x^2 = 18\cdot24\]

See also

1968 AHSME (ProblemsAnswer KeyResources)
Preceded by
Problem 23
Followed by
Problem 25
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 26 27 28 29 30
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