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Difference between revisions of "1985 AJHSME Problems/Problem 14"

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Line 11: Line 11:
 
<math>\text{(D)}</math> <dollar/><math>1</math>  
 
<math>\text{(D)}</math> <dollar/><math>1</math>  
  
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<math>\text{(E)}</math> <dollar/><math>10</math>
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<math>\text{(E)}</math> <dollar/><math>abefore tax is
  
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==Solution==
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</math>\text{(A)}<math> <dollar/></math>.01<math>
  
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The most straightforward method would be to calculate both prices, and subtract. But there's a better method...
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</math>\text{(B)}<math> <dollar/></math>.10<math>
 +
 +
</math>\text{(C)}<math> <dollar/></math>.50<math>
  
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Before we start, it's always good to convert the word problems into [[Expression|expressions]], we can solve.
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</math>\text{(D)}<math> <dollar/></math>1<math>
  
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So we know that the price of the object after a <math>6.5\% </math> increase will be <math>20 \times 6.5\% </math>, and the price of it after a <math>6\% </math> increase will be <math>20 \times 6\% </math>. And what we're trying to find is <math>6.5\% \times 20 - 6\% \times 20</math>, and if you have at least a little experience in the field of [[algebra]], you'll notice that both of the items have a common [[divisor|factor]], <math>20</math>, and we can [[factoring|factor]] the expression into
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</math>\text{(E)}<math> <dollar/></math>abefore tax is
−
<cmath>\begin{align*}
 
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(6.5\% - 6\% ) \times 20 &= (.5\% )\times 20 \\
 
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&= \frac{.5}{100}\times 20 \\
 
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&= \frac{1}{200}\times 20 \\
 
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&= .10 \\
 
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\end{align*}</cmath>
 
  
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<math>.10</math> is choice <math>\boxed{\text{B}}</math>
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<math>\text{(A)}</math> <dollar/><math>.01</math>  
  
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==See Also==
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<math>\text{(B)}</math> <dollar/><math>.10</math>
 +
 +
<math>\text{(C)}</math> <dollar/><math>.50</math>
  
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{{AJHSME box|year=1985|num-b=13|num-a=15}}
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<math>\text{(D)}</math> <dollar/><math>1</math>
−
[[Category:Introductory Algebra Problems]]
+
 
 +
<math>\text{(E)}</math> <dollar/><math>abefore tax is
 +
 
 +
</math>\text{(A)}<math> <dollar/></math>.01<math>
 +
 
 +
</math>\text{(B)}<math> <dollar/></math>.10<math>
 +
 +
</math>\text{(C)}<math> <dollar/></math>.50<math>
 +
 
 +
</math>\text{(D)}<math> <dollar/></math>1<math>
 +
 
 +
</math>\text{(E)}<math> <dollar/></math>abefore tax is
 +
 
 +
<math>\text{(A)}</math> <dollar/><math>.01</math>
 +
 
 +
<math>\text{(B)}</math> <dollar/><math>.10</math>
 +
 +
<math>\text{(C)}</math> <dollar/><math>.50</math>
 +
 
 +
<math>\text{(D)}</math> <dollar/><math>1</math>
 +
 
 +
<math>\text{(E)}</math> <dollar/>$a

Revision as of 09:32, 17 May 2009

Problem

The difference between a $6.5\%$ sales tax and a $6\%$ sales tax on an item priced at <dollar/>$20$ before tax is

$\text{(A)}$ <dollar/>$.01$

$\text{(B)}$ <dollar/>$.10$

$\text{(C)}$ <dollar/>$.50$

$\text{(D)}$ <dollar/>$1$

$\text{(E)}$ <dollar/>$abefore tax is$\text{(A)}$<dollar/>$.01$$ (Error compiling LaTeX. Unknown error_msg)\text{(B)}$<dollar/>$.10$$ (Error compiling LaTeX. Unknown error_msg)\text{(C)}$<dollar/>$.50$$ (Error compiling LaTeX. Unknown error_msg)\text{(D)}$<dollar/>$1$$ (Error compiling LaTeX. Unknown error_msg)\text{(E)}$<dollar/>$abefore tax is

$\text{(A)}$ <dollar/>$.01$

$\text{(B)}$ <dollar/>$.10$

$\text{(C)}$ <dollar/>$.50$

$\text{(D)}$ <dollar/>$1$

$\text{(E)}$ <dollar/>$abefore tax is$\text{(A)}$<dollar/>$.01$$ (Error compiling LaTeX. Unknown error_msg)\text{(B)}$<dollar/>$.10$$ (Error compiling LaTeX. Unknown error_msg)\text{(C)}$<dollar/>$.50$$ (Error compiling LaTeX. Unknown error_msg)\text{(D)}$<dollar/>$1$$ (Error compiling LaTeX. Unknown error_msg)\text{(E)}$<dollar/>$abefore tax is

$\text{(A)}$ <dollar/>$.01$

$\text{(B)}$ <dollar/>$.10$

$\text{(C)}$ <dollar/>$.50$

$\text{(D)}$ <dollar/>$1$

$\text{(E)}$ <dollar/>$a

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