document.write( "Question 623126: A piggy bank contains only quarters and nickels, and there is a total of 60 coins. The value of coins in the piggy bank is $7.40. How many quarters are in the piggy bank? \n" ); document.write( "
Algebra.Com's Answer #391996 by math-vortex(648) $\"\"$ $\"About$
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document.write( "Hi, there--\r\n" );
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document.write( "The Problem:\r\n" );
document.write( "A piggy bank contains only quarters and nickels, and there is a total of 60 coins. The value of coins in\r\n" );
document.write( "the piggy bank is $7.40. How many quarters are in the piggy bank?\r\n" );
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document.write( "A Solution:\r\n" );
document.write( "Let q be the number of quarters.\r\n" );
document.write( "Let n be the number  of nickels.\r\n" );
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document.write( "Now we need to write two equations using the information in the problem.\r\n" );
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document.write( "There is a total of 60 coins. In other words,\r\n" );
document.write( "[the number of quarters] + [the number of nickels] = [the total number of coins]\r\n" );
document.write( "In algebra , we write this relationship as\r\n" );
document.write( "q + n = 60\r\n" );
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document.write( "The value of the coins in the piggy bank is $7.40. In other words,\r\n" );
document.write( "[the value of the quarters] + [the value of the nickels] = [$7.40]\r\n" );
document.write( "The value of the quarters is 0.25 times the number of quarters, or 0.25q.\r\n" );
document.write( "The value of the nickels is 0.05 times the number of nickels, or 0.05n.\r\n" );
document.write( "In algebra, we write\r\n" );
document.write( "0.25q + 0.05n = 7.40\r\n" );
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document.write( "Now we have a system of equations with two variables. We will use the substitution method \r\n" );
document.write( "to solve for q and n.\r\n" );
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document.write( "Rearrange the first equation to a \"q=\" form. (Subtract n from both sides of the equation.\r\n" );
document.write( "q + n = 60\r\n" );
document.write( "q = 60 - n\r\n" );
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document.write( "We see that q and 60-n are equivalent. Substitute 60-n for q in the second equation.\r\n" );
document.write( "0.25q + 0.05n = 7.40\r\n" );
document.write( "0.25(60-n) + 0.05n = 7.40\r\n" );
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document.write( "Simplify and solve for n. Clear the parentheses.\r\n" );
document.write( "15 - 0.25n + 0.05n = 7.40\r\n" );
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document.write( "Combine like terms.\r\n" );
document.write( "15 - 0.20n = 7.40\r\n" );
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document.write( "Subtract 15 from both sides of the equation.\r\n" );
document.write( "-0.20n = 7.40 - 15\r\n" );
document.write( "-0.20n = -7.60\r\n" );
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document.write( "Divid both sides of the equation by -0.20.\r\n" );
document.write( "n = -7.60/-0.20\r\n" );
document.write( "n = 38.\r\n" );
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document.write( "There are 38 nickels. Since there are 60 coins altogether, there must be 60-38=22 quarters.\r\n" );
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document.write( "We need to check this number of each coin adds up to $7.40.\r\n" );
document.write( "38 nickels is 38*0.05 = $1.90\r\n" );
document.write( "22 quarters is 22*0.25 = $5.50\r\n" );
document.write( "$1.90+5.50 = $7.40.\r\n" );
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document.write( "Everything checks out; there are 22 quarters.\r\n" );
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document.write( "Feel free to email me if you have questions about the solution.\r\n" );
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document.write( "Ms.Figgy\r\n" );
document.write( "math.in.the.vortex@gmail.com\r\n" );
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