document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1204287>Question 1204287</A>: <I><SPAN STYLE=\"word-break: break-all;\"> There were some candies in a bag. Joseph took 7/10 of the candies and Kenny took the rest. Joseph took 24 more candies than Kenny.<BR>\n" );
document.write( "(a) What fraction of the candies did Kenny take?<BR>\n" );
document.write( "(b) How many candies were there in the bag at first? </SPAN>\n" );
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document.write( "k = amount of candies that Kenny took<BR>\n" );
document.write( "k+24 = amount of candies that Joseph took<BR>\n" );
document.write( "k is a positive integer\r<BR>\n" );
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document.write( "k+(k+24) = 2k+24 = total amount of candies\r<BR>\n" );
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document.write( "Joseph took 7/10 of this total.<BR>\n" );
document.write( "This must mean Kenny took 3/10 of the candies because<BR>\n" );
document.write( "1 - (7/10) = 3/10<BR>\n" );
document.write( "Think of a pizza with 10 slices. Joseph gets 7 slices and Kenny takes the remaining 3 slices.\r<BR>\n" );
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document.write( "(7/10)*total = amount Joseph took<BR>\n" );
document.write( "(7/10)*(2k+24) = k+24<BR>\n" );
document.write( "7(2k+24) = 10(k+24)<BR>\n" );
document.write( "14k+168 = 10k+240<BR>\n" );
document.write( "14k-10k = 240-168<BR>\n" );
document.write( "4k = 72<BR>\n" );
document.write( "k = 72/4<BR>\n" );
document.write( "k = 18\r<BR>\n" );
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document.write( "Or we could have these steps<BR>\n" );
document.write( "(3/10)*total = amount Kenny took<BR>\n" );
document.write( "(3/10)*(2k+24) = k<BR>\n" );
document.write( "3(2k+24) = 10k<BR>\n" );
document.write( "6k+72 = 10k<BR>\n" );
document.write( "72 = 10k-6k<BR>\n" );
document.write( "72 = 4k<BR>\n" );
document.write( "4k = 72<BR>\n" );
document.write( "k = 72/4<BR>\n" );
document.write( "k = 18<BR>\n" );
document.write( "Either way, Kenny took 18 candies.\r<BR>\n" );
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document.write( "k+24 = 18+24 = 42<BR>\n" );
document.write( "Joseph took 42 candies.<BR>\n" );
document.write( "In total there are 18+42 = 60 candies to start off.\r<BR>\n" );
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document.write( "7/10 of this is (7/10)*60 = 0.7*60 = 42 to represent how much Joseph took. We have confirmed the answers are correct.\r<BR>\n" );
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document.write( "Answers:<BR>\n" );
document.write( "(a) <font color=red size=4>3/10</font><BR>\n" );
document.write( "(b) <font color=red size=4>60 candies</font><BR>\n" );
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