document.write( "Question 168398: Can you help me get the answer and equation for this problem? \r
\n" ); document.write( "\n" ); document.write( "Penny collected some change in preparation for a garage sale. She collected two more nickels than twice the number of dimes and eight fewer quarters than twice the number of nickels. If the value of the quarters was $1.60 greater than four times the value of the nickels and dimes together, what was the total value of the change that Penny collected? \r
\n" ); document.write( "\n" ); document.write( " \n" ); document.write( "
Algebra.Com's Answer #124164 by ptaylor(2198)\"\" \"About 
You can put this solution on YOUR website!
Let x=number of nickels; 2x=twice the number of nickels; 2x-8 would be 8 fewer than twice the number of nickels
\n" ); document.write( "y=number of dimes; 2y=twice the number of dimes; 2y+2=2 more than twice the number of dimes
\n" ); document.write( "z=number of quarters\r
\n" ); document.write( "\n" ); document.write( "Now lets deal in pennies instead of $.
\n" ); document.write( "Value of the nickels=5x
\n" ); document.write( "Value of the dimes=10y
\n" ); document.write( "4 times the value of the nickels and dimes together=4(5x+10y)
\n" ); document.write( "Value of the quarters=25z\r
\n" ); document.write( "\n" ); document.write( "Now we are told the following:
\n" ); document.write( "x=2y+2 -------------------eq1
\n" ); document.write( "z=2x-8 ---------------------eq2
\n" ); document.write( "and
\n" ); document.write( "25z=4(5x+10y)+160-------------------------eq3\r
\n" ); document.write( "\n" ); document.write( "Lets rearrange and simplify the above equations so we can see what we are dealing with:
\n" ); document.write( "x-2y =2---------------------eq1
\n" ); document.write( "2x -z=8---------------------eq2
\n" ); document.write( "4x+8y-5z=-32-------------------eq3
\n" ); document.write( "Multiply eq1 by 4 and add it to
\n" ); document.write( "eq3 and we get:
\n" ); document.write( "8x-5z=-24----------------------------eq3a
\n" ); document.write( "Next multiply eq2 by 4 and subtract it from eq3a and we get\r
\n" ); document.write( "\n" ); document.write( "(8x-5z+-24) -(8x-4z=32) or
\n" ); document.write( "-z=-56
\n" ); document.write( "z=56-------------------------------------------number of quarters
\n" ); document.write( "substitute z=56 into eq2 and we get:
\n" ); document.write( "2x-56=8
\n" ); document.write( "2x=64
\n" ); document.write( "x=32-------------------------------------number of nickels
\n" ); document.write( "substitute x=32 into eq1 and we get:
\n" ); document.write( "32-2y=2
\n" ); document.write( "-2y=-30
\n" ); document.write( "y=15------------------------------------- number of dimes
\n" ); document.write( "CK
\n" ); document.write( "two more nickels than twice the number of dimes:
\n" ); document.write( "2*15+2=32
\n" ); document.write( "32=32
\n" ); document.write( "eight fewer quarters than twice the number of nickels:
\n" ); document.write( "32*2-8=56
\n" ); document.write( "56=56
\n" ); document.write( "value of the quarters was $1.60 greater than four times the value of the nickels and dimes together:
\n" ); document.write( "56*25=4(32*5+15*10)+160
\n" ); document.write( "1400=4(160+150)+160=(4*310)+160
\n" ); document.write( "1400=1240+160=1400
\n" ); document.write( "1400=1400\r
\n" ); document.write( "\n" ); document.write( "Hope this helps-----ptaylor\r
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