document.write( "Question 1045320: LAST season,a pair of jeans cost $35.00, this season the pair of jeans increased by 25%, Later in the season the jeans were put on sale for 25% off. How much did the jeans cost at the beginning of the season? And what was their sale price? Where you surprised by the sale price of the jeans? Why or why not? What would the jeans cost if they had gone on sale by 25% first, and then had their price increased by 25%? Why? \n" ); document.write( "

Algebra.Com's Answer #660726 by KMST(5328) $\"\"$ $\"About$

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Percentages are ratios, and sometimes we can write them as decimals: $\"%2225%25%22=25%2F100=0.25\"$ .
\n" ); document.write( "At the beginning of this season the price of the jeans had increased from $\"%22%2435%22\"$ by
\n" ); document.write( " $\"0.25%2A%22%2435%22=%22%248.75%22\"$ .
\n" ); document.write( "So, at the beginning of this season the price of the jeans was
\n" ); document.write( " $\"%22%2435%22%2B%22%248.75%22=highlight%28%22%2443.75%22%29\"$ .
\n" ); document.write( "When, later in the season. the jeans were put on sale for 25% off, the discount was $\"0.25%2A%22%2443.75%22=%22%2410.9375%22\"$ ,
\n" ); document.write( "so the new, sale price was calculated as
\n" ); document.write( " $\"%22%2443.75%22-%22%2410.9375%22=%22%2432.8125%22\"$ ,
\n" ); document.write( "which should have been rounded to $\"highlight%28%22%2432.81%22%29\"$ .\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "We should not be surprised to see that 25% of a lower starting price
\n" ); document.write( "is less than 25% of a higher price.
\n" ); document.write( "When the price is first increased by 25%, the increase is $\"0.25=1%2F4\"$ of just $\"%22%2435%22\"$ ,
\n" ); document.write( "but when they apply the 25% discount to the larger jacked up price, the discount is $\"0.25=1%2F4\"$ of a larger amount.
\n" ); document.write( "Of course, the final price will be lower than the fist price.\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "Of course, if the starting price had been cut by 25% first, to get a smaller second price,
\n" ); document.write( "adding 25% of that smaller price later would have been adding a lesser mark up, and the final price would have been less.
\n" ); document.write( "Why? Because the initial discount and the final price increase were calculated as the same percentage base on different prices,
\n" ); document.write( "and when you apply the discount first,
\n" ); document.write( "you get a smaller price that is used to calculate a smaller price increase. \n" ); document.write( "

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