document.write( "Question 1028682: If one group had 3 car washes, 2 bake sales and 5 dances to make $31, and the next had 5 car washes with 5 bake sales and 7 dances to make $56 and the last group had 7 car washes and 3 bake sales and 10 dances for $59 , how much was each cw, bs and d \n" ); document.write( "

Algebra.Com's Answer #643793 by addingup(3677) $\"\"$ $\"About$

You can put this solution on YOUR website!
car wash: x
\n" ); document.write( "bake sale: y
\n" ); document.write( "dances: z
\n" ); document.write( "````````````````````````````````````````
\n" ); document.write( "3x+2y+5z = 31
\n" ); document.write( "5x+5y+7z = 56
\n" ); document.write( "7x+3y+10z = 59
\n" ); document.write( "So now we have a system of equations.
\n" ); document.write( "``````````````````````````````````````````````
\n" ); document.write( "Multiply the first equation times 5:
\n" ); document.write( "(3x+2y+5z = 31)*5 = 15x+10y+25z = 155
\n" ); document.write( "Multiply the second equation times 3:
\n" ); document.write( "(5x+5y+7z = 56)*3 = 15x+15y+21z = 168
\n" ); document.write( "Subtract:
\n" ); document.write( "15x+15y+21z = 168
\n" ); document.write( "-
\n" ); document.write( "15x+10y+25z = 155
\n" ); document.write( "------------------
\n" ); document.write( "5y-4z = 13
\n" ); document.write( "Our new set of equations:
\n" ); document.write( "15x+10y+25z = 155
\n" ); document.write( "5y-4z = 13
\n" ); document.write( "7x+3y+10z = 59
\n" ); document.write( "`````````````````````````````````````
\n" ); document.write( "Multiply the first equation times 7:
\n" ); document.write( "(15x+10y+25z = 155)*7 = 105x+70y+175z = 1085
\n" ); document.write( "Multiply the third equation times 15:
\n" ); document.write( "(7x+3y+10z = 59)*15 = 105x+45y+150z=885
\n" ); document.write( "Subtract:
\n" ); document.write( "105x+45y+150z=885
\n" ); document.write( "-
\n" ); document.write( "105x+70y+175z = 1085
\n" ); document.write( "---------------------
\n" ); document.write( "-25y-25z = -200
\n" ); document.write( "New set of equations:
\n" ); document.write( "105x+70y+175z = 1085
\n" ); document.write( "5y-4z = 13
\n" ); document.write( "-25y-25z = -200
\n" ); document.write( "``````````````````````````````````````
\n" ); document.write( "Multiply the second equation times 5:
\n" ); document.write( "(5y-4z = 13)*5 = 25y-20z=65
\n" ); document.write( "Subtract:
\n" ); document.write( "-25y-25z = -200
\n" ); document.write( "-
\n" ); document.write( "25y-20z = 65
\n" ); document.write( "------------
\n" ); document.write( "-45z = -135
\n" ); document.write( "New set of equations:
\n" ); document.write( "105x+70y+175z = 1085
\n" ); document.write( "25y-20z = 65
\n" ); document.write( "-45z = -135
\n" ); document.write( "Solve for z:
\n" ); document.write( "-45z = -135 divide both sides by -45 and remember -/- = +
\n" ); document.write( "z = 3
\n" ); document.write( "Now solve for y:
\n" ); document.write( "25y-20(3) = 65
\n" ); document.write( "25y-60 = 65
\n" ); document.write( "25y = 125
\n" ); document.write( "y = 5
\n" ); document.write( "Now solve for x:
\n" ); document.write( "105x+70y+175z = 1085 you do this one. Email me if you get stock.
\n" ); document.write( "John\r
\n" ); document.write( "\n" ); document.write( " \n" ); document.write( "

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