document.write( "Question 225843: ECE Board November 1999/2000 In a box, there are 25 coins consisting of quarter, nickels and dimes with a total amount of $2.75. if the nickel were dimes ad the dimes were quarters and the quarters were nickles, the total amount would be $3.75. how many quarters are there? note:Nickel = 5cents, dime = 10 cents and quarter = 25 cents. \n" ); document.write( "
Algebra.Com's Answer #168383 by ankor@dixie-net.com(22740)\"\" \"About 
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In a box, there are 25 coins consisting of quarter, nickels and dimes with a total amount of $2.75.
\n" ); document.write( " if the nickels were dimes, and the dimes were quarters, and the quarters were nickels, the total amount would be $3.75.
\n" ); document.write( "how many quarters are there?
\n" ); document.write( ":
\n" ); document.write( "Originally x=no.of nickels, y=dimes, z=quarters
\n" ); document.write( ":
\n" ); document.write( "Three equations:
\n" ); document.write( "x + y + z = 25
\n" ); document.write( ":
\n" ); document.write( "5x + 10y + 25z = 275; using cents
\n" ); document.write( ":
\n" ); document.write( "25x + 5y + 10z = 375
\n" ); document.write( ":
\n" ); document.write( "Multiply the 1st equation by 5, subtract from the 2nd equation
\n" ); document.write( "5x + 10y + 25z = 275
\n" ); document.write( "5x + 5y + 5z = 125
\n" ); document.write( "-----------------------eliminate x
\n" ); document.write( "5y + 20z = 150
\n" ); document.write( "simplify, divide by 5
\n" ); document.write( "y + 4z = 30
\n" ); document.write( ":
\n" ); document.write( "Multiply 1st equation by 25, subtract the 3rd equation
\n" ); document.write( "25x + 25y + 25z = 625
\n" ); document.write( "25x + 5y + 10z = 375
\n" ); document.write( "------------------------eliminate x again
\n" ); document.write( " 20y + 15z = 250
\n" ); document.write( "Simplify, divide by 5
\n" ); document.write( "4y + 3z = 50
\n" ); document.write( ":
\n" ); document.write( "We have two, 2 unknown equations
\n" ); document.write( " y + 4z = 30
\n" ); document.write( "4y + 3z = 50
\n" ); document.write( ":
\n" ); document.write( "Multiply the 1st equation by 4, subtract the 2nd
\n" ); document.write( "4y + 16z = 120
\n" ); document.write( "4y + 3z = 50
\n" ); document.write( ":
\n" ); document.write( "There is something wrong with this problem, it does not have integer solutions
\n" ); document.write( " \n" ); document.write( "
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