document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1120734>Question 1120734</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A motorist reduces his annual distance travel by x% when the price of petrol is increased by y%. Find the increase percent in his petrol bill. </SPAN>\n" );
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document.write( "The distance traveled (and therefore presumably the amount of petrol used) is multiplied by a factor of (1-x/100); the price is multiplied by a factor of (1+y/100).  The total cost of the petrol is<br><BR>\n" );
document.write( "(1-x/100)(1+y/100) = 1+y/100-x/100-xy/10000<br><BR>\n" );
document.write( "The change in the cost of the petrol is<br><BR>\n" );
document.write( "y/100-x/100-xy/10000<br><BR>\n" );
document.write( "Multiplying by 100 to get the change as a percentage, the percent change in the cost is y-x-xy/100.<br><BR>\n" );
document.write( "Note we don't know whether that is an increase or a decrease in total cost.<br><BR>\n" );
document.write( "Example 1:<BR>\n" );
document.write( "Decrease travel by 10% when the price increases by 20% (x=10,y=20)<BR>\n" );
document.write( "The distance traveled gets multiplied by (1-.10) = .90; the price gets multiplied by (1+.20) = 1.20<BR>\n" );
document.write( "The total cost gets multiplied by (.90)(1.20) = 1.08, an increase of 8%<BR>\n" );
document.write( "By the formula, 20-10-200/100 = 10-2 = 8 percent<br><BR>\n" );
document.write( "Example 2:<BR>\n" );
document.write( "Decrease travel by 30% when the cost increases by 10% (x=30, y=10)<BR>\n" );
document.write( "The distance traveled gets multiplied by (1-.30) = .70; the price gets multiplied by (1+.10) = 1.10<BR>\n" );
document.write( "The total cost gets multiplied by (.70)(1.10) = 0.77, an decrease of 23%<BR>\n" );
document.write( "By the formula, 10-30-300/100 = -20-3 = -23 percent<br> </SPAN>\n" );
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