Difference between revisions of "2002 AMC 8 Problems/Problem 14"

(Solution #2)
(Solution #1)
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==Solution #1==
 
==Solution #1==
  
Let's assume that each item is <math>&#036;100</math>. First we take off <math>30\%</math> off of <math>&#036;100</math> <math>&#036;100\cdot0.70=&#036;70</math>
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Let's assume that each item is &#036;100. First we take off <math>30\%</math> off of &#036;100. &#036;100\cdot0.70=<math> &#036;70
  
Next, we take off the extra <math>20\%</math> as asked by the problem. <math>&#036;70\cdot0.80=&#036;56</math>
+
Next, we take off the extra </math>20\%<math> as asked by the problem. &#036;70\cdot0.80=&#036;56
  
So the final price of an item is <math>&#036;56</math>. We have to do <math>100-56</math> because <math>56</math> was the final price and we wanted the discount.
+
So the final price of an item is &#036;56. We have to do </math>100-56<math> because </math>56<math> was the final price and we wanted the discount.
  
<math>100-56=44</math> so the final discount was <math>44\%</math>
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</math>100-56=44<math> so the final discount was </math>44\%<math>
  
<math> \text{(A)}\ 35\%\qquad\boxed{\text{(B)}\ 44\%}\qquad\text{(C)}\ 50\%\qquad\text{(D)}\ 56\%\qquad\text{(E)}\ 60\% </math>
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</math> \text{(A)}\ 35\%\qquad\boxed{\text{(B)}\ 44\%}\qquad\text{(C)}\ 50\%\qquad\text{(D)}\ 56\%\qquad\text{(E)}\ 60\% $
  
 
==Solution #2==
 
==Solution #2==

Revision as of 21:09, 29 July 2012

Problem 14

A merchant offers a large group of items at $30\%$ off. Later, the merchant takes $20\%$ off these sale prices and claims that the final price of these items is $50\%$ off the original price. The total discount is


$\text{(A)}\ 35\%\qquad\text{(B)}\ 44\%\qquad\text{(C)}\ 50\%\qquad\text{(D)}\ 56\%\qquad\text{(E)}\ 60\%$

Solution #1

Let's assume that each item is $100. First we take off $30\%$ off of $100. $100\cdot0.70=$&#036;70

Next, we take off the extra$ (Error compiling LaTeX. ! Missing $ inserted.)20\%$as asked by the problem. &#036;70\cdot0.80=&#036;56

So the final price of an item is &#036;56. We have to do$ (Error compiling LaTeX. ! Missing $ inserted.)100-56$because$56$was the final price and we wanted the discount.$100-56=44$so the final discount was$44\%$$ (Error compiling LaTeX. ! Missing $ inserted.) \text{(A)}\ 35\%\qquad\boxed{\text{(B)}\ 44\%}\qquad\text{(C)}\ 50\%\qquad\text{(D)}\ 56\%\qquad\text{(E)}\ 60\% $

Solution #2

Assume the price was $100. We can just do $100\cdot0.7\cdot0.8=56$ and then do $100-56=44$ That is the discount percentage wise.

$\text{(A)}\ 35\%\qquad\boxed{\text{(B)}\ 44\%}\qquad\text{(C)}\ 50\%\qquad\text{(D)}\ 56\%\qquad\text{(E)}\ 60\%$

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