document.write( "Question 295711: A shopkeeper gives two successive discounts of 8% and 12%. What is overall discount? plz hlp me ans is 33.33% \n" ); document.write( "

Algebra.Com's Answer #213137 by jim_thompson5910(35256) $\"\"$ $\"About$

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Let 'x' be the original price. If you apply an 8% discount, you're basically subtracting 8% of the original price from the original price. In other words, you're doing $\"x-0.08x=0.92x\"$ \r
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\n" ); document.write( "\n" ); document.write( "So after an 8% discount, the new price is $\"0.92x\"$ dollars. Now apply the 12% discount using similar logic to get $\"0.92x-0.12%280.92x%29=0.92x-0.1104x=0.8096x\"$ \r
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\n" ); document.write( "\n" ); document.write( "So after applying the 8% discount, then the 12% discount, the final sale price is $\"0.8096x\"$ . Subtract the coefficient from 1 to get $\"1-0.8096=0.1904\"$ and then multiply that result by 100 to get 19.04%\r
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\n" ); document.write( "\n" ); document.write( "So the overall discount is 19.04%\r
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\n" ); document.write( "\n" ); document.write( "Example: Say an item originally costs $100. Apply the 8% discount to get $\"0.92%28100%29=92\"$ (note: think of it as subtracting $8, 8% of $100, from $100). So after the first discount, the sale price is $92. Now apply the 12% discount to the new price of $92 to get $\"92-0.12%2892%29=92-11.04=80.96\"$ . This means that after the two discounts, the final price is $80.96\r
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\n" ); document.write( "\n" ); document.write( "Instead of taking two steps to find the final discount, we can take a shortcut and simply apply the overall discount of 19.04% (we should get the same answer if we did things right). So applying the discount of 19.04% to the original price of $100 gets us $\"100-0.1904%28100%29=100-19.04=80.96\"$ which is what got earlier. So this example helps support our answer. Try other values to confirm for yourself that this is the right discount. Try to incorporate real world values (ie prices you might see in the grocery store) to help you see that it works. As you can see, it's very useful to be able to combine multiple discounts into one to save time and avoid errors. \n" ); document.write( "

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