document.write( "Question 51864: I'm having trouble with a word problem. It is a Number Problem, You have $30 in change in your drawer, consisting of dimes and quarters. write an inequity that shows the different number of coins in your drawer. I hinestly do do not know even where to begin. Please Help. \n" ); document.write( "
Algebra.Com's Answer #34590 by AnlytcPhil(1806)\"\" \"About 
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I'm having trouble with a word problem. It is a Number Problem, You have $30 in\r\n" );
document.write( "change in your drawer, consisting of dimes and quarters. write an inequity that\r\n" );
document.write( "shows the different number of coins in your drawer. I honestly do do not know\r\n" );
document.write( "even where to begin. Please Help.\r\n" );
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document.write( "There must be some quarters among your $30 in change, for if there were no\r\n" );
document.write( "quarters, and all were dimes (300 of them), your $30 wouldn't consist of dimes\r\n" );
document.write( "AND QUARTERS, but only of dimes.\r\n" );
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document.write( "The most dimes you could have would be when you have the least possible number\r\n" );
document.write( "of quarters.\r\n" );
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document.write( "You can't have just one quarter because that would leave $29.75 to have all in\r\n" );
document.write( "dimes, and you can't have that because you would need a nickel, but you don't\r\n" );
document.write( "have any nickels!\r\n" );
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document.write( "But you can have as few as two quarters, because that would leave $29.50 which\r\n" );
document.write( "you could have with 295 dimes.\r\n" );
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document.write( "So the least number of quarters you could have would be 2 and the most number\r\n" );
document.write( "of dimes you could have is 295\r\n" );
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document.write( "Therefore if D represents the number of dimes, then D is less than or equal to\r\n" );
document.write( "295, so the way to write that as an inequality is\r\n" );
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document.write( "               D < 295\r\n" );
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document.write( "and if Q represents the number of quarters, then since there must be at least\r\n" );
document.write( "two quarters, the way to write that as an inequality is\r\n" );
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document.write( "               Q > 2\r\n" );
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document.write( "Now we'll go the other way:\r\n" );
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document.write( "There must be some dimes among your $30 in change, for if there were no dimes,\r\n" );
document.write( "and all were quarters (120 of them), your $30 wouldn't consist of dimes and\r\n" );
document.write( "quarters, but only of quarters.\r\n" );
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document.write( "The most quarters you could have would be when you have the least possible\r\n" );
document.write( "number of dimes.\r\n" );
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document.write( "You can't have just one dime because that would leave $29.90 and you can't have\r\n" );
document.write( "that all in quarters. Neither can you have $29.80, nor $29.70, nor $29.60 only\r\n" );
document.write( "in quarters. However you can have $29.50 with 118 quarters (which means you\r\n" );
document.write( "must have at least 5 dimes). \r\n" );
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document.write( "Therefore the least number of dimes you can have is 5 and the most number of\r\n" );
document.write( "quarters you can have is 118.\r\n" );
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document.write( "Therefore since Q represents the number of quarters, then Q is less than or\r\n" );
document.write( "equal to 118, so the way to write that as an inequality is\r\n" );
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document.write( "               Q < 118\r\n" );
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document.write( "and since D represents the number of dimes, then since there must be at least 5\r\n" );
document.write( "dimes, the way to write that as an inequality is\r\n" );
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document.write( "               D > 5\r\n" );
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document.write( "Putting all the inequalities together:\r\n" );
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document.write( "               D < 295\r\n" );
document.write( "               Q > 2\r\n" );
document.write( "               Q < 118\r\n" );
document.write( "               D > 5\r\n" );
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document.write( "Turn the 2nd and 4th inequalities backward, so they'll all be \"less than\r\n" );
document.write( "or equal\"'s\r\n" );
document.write( "               D < 295\r\n" );
document.write( "               2 < Q\r\n" );
document.write( "               Q < 118\r\n" );
document.write( "               5 < D\r\n" );
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document.write( "Now we can combine the 4th and 1st of these with D in \r\n" );
document.write( "the middle as\r\n" );
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document.write( "             5 < D < 295\r\n" );
document.write( "               \r\n" );
document.write( "We can combine the 2nd and 3rd with Q in the middle as\r\n" );
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document.write( "             2 < Q < 118\r\n" );
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document.write( "Edwin
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