document.write( "Question 82709This question is from textbook
\n" ); document.write( ": A certain brand of razor blades comes in packages of 6, 12, and 24 blades, costing $2, $3, and $4 per package, respectively. A store sold 12 packages containing a total of 162 razor blades and took in $35 dollars. How many packages of each type were sold? \n" ); document.write( "
Algebra.Com's Answer #59372 by ankor@dixie-net.com(22740)\"\" \"About 
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A certain brand of razor blades comes in packages of 6, 12, and 24 blades, costing $2, $3, and $4 per package, respectively. A store sold 12 packages containing a total of 162 razor blades and took in $35 dollars. How many packages of each type were sold?
\n" ); document.write( ":
\n" ); document.write( "Let x = no. of 6 blade pkgs
\n" ); document.write( "Let y = no. of 12 blade pkgs
\n" ); document.write( "Let z = no. of 24 blade pkgs
\n" ); document.write( ":
\n" ); document.write( "The no. of pkgs equation:
\n" ); document.write( "x + y + z = 12
\n" ); document.write( ":
\n" ); document.write( "The total cost equation:
\n" ); document.write( "2x + 3y + 4z = 35
\n" ); document.write( ":
\n" ); document.write( "The no. of blades equation
\n" ); document.write( "6x + 12y + 24z = 162
\n" ); document.write( ":
\n" ); document.write( "Multiply the 1st equation by 2 and subtract it from eq 2:
\n" ); document.write( "2x + 3y + 4z = 35
\n" ); document.write( "2x + 2y + 2z = 24
\n" ); document.write( "--------------------subtracting eliminates x
\n" ); document.write( "0x + 1y + 2z = 11
\n" ); document.write( "y + 2z = 11
\n" ); document.write( "y = (11 - 2z); we use this for substitution
\n" ); document.write( ":
\n" ); document.write( "Multiply equation 1 by 6 and subtract it from equation 3
\n" ); document.write( "6x + 12y + 24z = 162
\n" ); document.write( "6x + 6y + 6z = 72
\n" ); document.write( "---------------------subtracting eliminates x again
\n" ); document.write( "0x + 6y + 18z = 90
\n" ); document.write( "6y + 18z = 90
\n" ); document.write( ":
\n" ); document.write( "Substitute (11-2z) for y in the above equation, find z
\n" ); document.write( "6(11-2z) + 18z = 90
\n" ); document.write( "66 - 12z + 18z = 90
\n" ); document.write( "6z = 90 - 66
\n" ); document.write( "6z = 24
\n" ); document.write( "z = 24/6
\n" ); document.write( "z = 4 ea 24 blade pkgs
\n" ); document.write( ":
\n" ); document.write( "y = 11 - 2z
\n" ); document.write( "y = 11 - 2(4)
\n" ); document.write( "y = 11 - 8
\n" ); document.write( "y = 3 ea 12 blade pkgs
\n" ); document.write( ":
\n" ); document.write( "Let you figure out what x is using the 1st equation:
\n" ); document.write( ":
\n" ); document.write( "Check solutions in the 3rd equation: \n" ); document.write( "
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