https://artofproblemsolving.com/wiki/api.php?action=feedcontributions&user=Akhil27&feedformat=atom AoPS Wiki - User contributions [en] 2022-01-27T20:24:24Z User contributions MediaWiki 1.31.1 https://artofproblemsolving.com/wiki/index.php?title=2002_AMC_8_Problems/Problem_14&diff=120398 2002 AMC 8 Problems/Problem 14 2020-04-02T13:17:50Z <p>Akhil27: /* Solution */</p> <hr /> <div>== Problem ==<br /> <br /> A merchant offers a large group of items at &lt;math&gt;30\%&lt;/math&gt; off. Later, the merchant takes &lt;math&gt;20\%&lt;/math&gt; off these sale prices and claims that the final price of these items is &lt;math&gt;50\%&lt;/math&gt; off the original price. The total discount is<br /> <br /> <br /> &lt;math&gt; \text{(A)}\ 35\%\qquad\text{(B)}\ 44\%\qquad\text{(C)}\ 50\%\qquad\text{(D)}\ 56\%\qquad\text{(E)}\ 60\% &lt;/math&gt;<br /> <br /> ==Solution==<br /> ===Solution 1===<br /> <br /> Let's assume that each item is &lt;math&gt;100&lt;/math&gt; dollars. First we take off &lt;math&gt;30\%&lt;/math&gt; off of &lt;math&gt;100&lt;/math&gt; dollars. &lt;math&gt;100\cdot0.7=70&lt;/math&gt;<br /> <br /> Next, we take off the extra &lt;math&gt;20\%&lt;/math&gt; as asked by the problem. &lt;math&gt;70\cdot0.80=56&lt;/math&gt;<br /> <br /> So the final price of an item is \$56. We have to do &lt;math&gt;100-56&lt;/math&gt; because &lt;math&gt;56&lt;/math&gt; was the final price and we wanted the discount.<br /> <br /> &lt;math&gt;100-56=44&lt;/math&gt; so the final discount was &lt;math&gt;\boxed{\text{(B)}\ 44\%}&lt;/math&gt;.<br /> <br /> ===Solution 2===<br /> <br /> Assume the price was \$100. We can just do &lt;math&gt;100\cdot0.7\cdot0.8=56&lt;/math&gt; and then do &lt;math&gt;100-56=\boxed{\text{(B)}\ 44}&lt;/math&gt;. That is the discount percentage wise.<br /> <br /> ==See Also==<br /> {{AMC8 box|year=2002|num-b=13|num-a=15}}<br /> {{MAA Notice}}</div> Akhil27