https://artofproblemsolving.com/wiki/api.php?action=feedcontributions&user=Giga&feedformat=atomAoPS Wiki - User contributions [en]2024-03-28T10:13:14ZUser contributionsMediaWiki 1.31.1https://artofproblemsolving.com/wiki/index.php?title=2002_AMC_8_Problems/Problem_14&diff=1384722002 AMC 8 Problems/Problem 142020-11-25T18:59:34Z<p>Giga: /* Solution 2 */</p>
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<div>== Problem ==<br />
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A merchant offers a large group of items at <math>30\%</math> off. Later, the merchant takes <math>20\%</math> off these sale prices and claims that the final price of these items is <math>50\%</math> off the original price. The total discount is<br />
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<math> \text{(A)}\ 35\%\qquad\text{(B)}\ 44\%\qquad\text{(C)}\ 50\%\qquad\text{(D)}\ 56\%\qquad\text{(E)}\ 60\% </math><br />
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==Solution==<br />
===Solution 1===<br />
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Let's assume that each item is <math>100</math> dollars. First we take off <math>30\%</math> off of <math>100</math> dollars. <math>100\cdot0.7=70</math><br />
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Next, we take off the extra <math>20\%</math> as asked by the problem. <math>70\cdot0.80=56</math><br />
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So the final price of an item is \$56. We have to do <math>100-56</math> because <math>56</math> was the final price and we wanted the discount.<br />
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<math>100-56=44</math> so the final discount was <math>\boxed{\text{(B)}\ 44\%}</math>.<br />
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===Solution 2===<br />
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Assume the price was \$100. We can just do <math>100\cdot0.7\cdot0.8=56</math> and then do <math>100-56=\boxed{\text{(B)}\ 44\%}</math>. That is the discount percentage wise.<br />
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==See Also==<br />
{{AMC8 box|year=2002|num-b=13|num-a=15}}<br />
{{MAA Notice}}</div>Giga