document.write( "Question 1006741: Momo has nickels, Koko has dimes, and Dodo has quarters. Koko has 5 more dimes than Dodo has quarters. If Momo gives Koko a nickel, Koko gives Dodo a dime, and Dodo gives Momo a quarter. How many coins did each originally have?\r
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Algebra.Com's Answer #622863 by Edwin McCravy(20054)![]() ![]() You can put this solution on YOUR website! Momo has nickels, Koko has dimes, and Dodo has quarters. Koko has 5 \n" ); document.write( "more dimes than Dodo has quarters. If Momo gives Koko a nickel, Koko \n" ); document.write( "gives Dodo a dime, and Dodo gives Momo a quarter. How many coins did \n" ); document.write( "each originally have? \n" ); document.write( " \r\n" ); document.write( "Apparently something has been left out of the problem. I will assume\r\n" ); document.write( "what was left out is what is in red below:\r\n" ); document.write( " \n" ); document.write( "Momo has nickels, Koko has dimes, and Dodo has quarters. Koko has 5 \n" ); document.write( "more dimes than Dodo has quarters. If Momo gives Koko a nickel, Koko \n" ); document.write( "gives Dodo a dime, and Dodo gives Momo a quarter, then they all end \n" ); document.write( "up with the same mount of money. How many coins did each originally \n" ); document.write( "have? \n" ); document.write( " \r\n" ); document.write( "Momo has m nickels or 5m cents originally\r\n" ); document.write( "\r\n" ); document.write( "Koko has k dimes or 10k cents originally\r\n" ); document.write( "\r\n" ); document.write( "Dodo has d quarters or 25d cents originally\r\n" ); document.write( " \n" ); document.write( ">>Koko has 5 more dimes than Dodo has quarters.<< \n" ); document.write( " \r\n" ); document.write( "Then k = d+5\r\n" ); document.write( " \n" ); document.write( ">>If Momo gives Koko a nickel,<< \n" ); document.write( " \r\n" ); document.write( "Then Momo has 5m-5 cents and Koko has 10k+5 cents \r\n" ); document.write( " \n" ); document.write( ">>Koko gives Dodo a dime,<< \n" ); document.write( " \r\n" ); document.write( "Then Koko has 10k+5-10 cents or 10k-5 cents and \r\n" ); document.write( "Dodo has 25d+10 cents\r\n" ); document.write( " \n" ); document.write( ">>and Dodo gives Momo a quarter,<< \n" ); document.write( " \r\n" ); document.write( "Then Dodo has 15d+10-25 cents or 15d-15 cents and \r\n" ); document.write( "Momo has 5m-5+25 cents or 5m+20 cents\r\n" ); document.write( "\r\n" ); document.write( "So we have\r\n" ); document.write( "\r\n" ); document.write( "k = d+5\r\n" ); document.write( "Momo ends up with 5m+20 cents\r\n" ); document.write( "Dodo ends up with 15d-15 cents\r\n" ); document.write( "Koko ends up with 10k-5 cents\r\n" ); document.write( " \n" ); document.write( ">>, then they all end up with the same amount of money.<< \n" ); document.write( " \r\n" ); document.write( "5m+20 = 15d-15 = 10k-5\r\n" ); document.write( "\r\n" ); document.write( "Substituting d+5 for k\r\n" ); document.write( "\r\n" ); document.write( "5m+20 = 15d-15 = 10(d+5)-5\r\n" ); document.write( " 15d-15 = 10d+50-5\r\n" ); document.write( " 15d-15 = 10d+45\r\n" ); document.write( " 5d = 60\r\n" ); document.write( " d = 12, so Dodo had 12 quarters originally.\r\n" ); document.write( "\r\n" ); document.write( "Substituting in k = d+5\r\n" ); document.write( "\r\n" ); document.write( "k = 12+5 = 17, so Koko had 17 dimes originally.\r\n" ); document.write( "\r\n" ); document.write( "Substituting in 5m+20 = 15d-15\r\n" ); document.write( "\r\n" ); document.write( "5m+20 = 15(12)-15\r\n" ); document.write( "5m+20 = 165\r\n" ); document.write( " 5m = 145\r\n" ); document.write( " m = 29 so Momo had 29 nickels originally.\r\n" ); document.write( "\r\n" ); document.write( "Edwin\n" ); document.write( " |