document.write( "Question 110385: Help needed please
\n" ); document.write( "Find X, Y, and Z
\n" ); document.write( "X + Y + Z =1150
\n" ); document.write( "X = 4Z + 100
\n" ); document.write( "X = 6Y + 50\r
\n" ); document.write( "\n" ); document.write( "thank you \n" ); document.write( "

Algebra.Com's Answer #80445 by Edwin McCravy(20056) $\"\"$ $\"About$

You can put this solution on YOUR website!
Help needed please
\n" ); document.write( "Find X, Y, and Z\r
\n" ); document.write( "\n" ); document.write( "X + Y + Z = 1150
\n" ); document.write( "X = 4Z + 100
\n" ); document.write( "X = 6Y + 50 \r
\n" ); document.write( "\n" ); document.write( "Solve the 2nd eq for Z:\r
\n" ); document.write( "\n" ); document.write( " X = 4Z + 100
\n" ); document.write( " X - 100 = 4Z\r
\n" ); document.write( "\n" ); document.write( "Divide every term by 4\r
\n" ); document.write( "\n" ); document.write( " $\"X%2F4\"$ - $\"100%2F4\"$ = $\"%284Z%29%2F4\"$
\n" ); document.write( " $\"X%2F4\"$ - $\"25\"$ = $\"Z\"$
\n" ); document.write( " $\"Z\"$ = $\"X%2F4\"$ - $\"25\"$
\n" ); document.write( "Solve the 3rd eq for Y:\r
\n" ); document.write( "\n" ); document.write( " X = 6Y + 50
\n" ); document.write( " X - 50 = 6Y\r
\n" ); document.write( "\n" ); document.write( "Divide every term by 6\r
\n" ); document.write( "\n" ); document.write( " $\"X%2F6\"$ - $\"50%2F6\"$ = $\"%286Y%29%2F6\"$
\n" ); document.write( " $\"X%2F6\"$ - $\"25%2F3\"$ = $\"Y\"$
\n" ); document.write( " $\"Y\"$ = $\"X%2F6\"$ - $\"25%2F3\"$ \r
\n" ); document.write( "\n" ); document.write( "Substitute $\"Y\"$ = $\"X%2F6\"$ - $\"25%2F3\"$
\n" ); document.write( "and $\"Z\"$ = $\"X%2F4\"$ - $\"25\"$
\n" ); document.write( "into the first equation:\r
\n" ); document.write( "\n" ); document.write( "X + Y + Z = 1150
\n" ); document.write( "X + ( $\"X%2F6\"$ - $\"25%2F3\"$ ) + ( $\"X%2F4\"$ - $\"25\"$ ) = 1150
\n" ); document.write( "X + $\"X%2F6\"$ - $\"25%2F3\"$ + $\"X%2F4\"$ - $\"25\"$ = 1150
\n" ); document.write( "Nultiply every term by 12\r
\n" ); document.write( "\n" ); document.write( "12·X + 12· $\"X%2F6\"$ - 12· $\"25%2F3\"$ + 12· $\"X%2F4\"$ - 12· $\"25\"$ = 12·1150\r
\n" ); document.write( "\n" ); document.write( "12X + 2X - 100 + 3X - 300 = 13800
\n" ); document.write( " 17X - 400 = 13800
\n" ); document.write( " 17X = 13800 + 400
\n" ); document.write( " 17X = 14200
\n" ); document.write( " X = $\"14200%2F17\"$ \r
\n" ); document.write( "\n" ); document.write( "Substitute X = $\"14200%2F17\"$ in X = 6Y + 50\r
\n" ); document.write( "\n" ); document.write( " X = 6Y + 50
\n" ); document.write( " $\"14200%2F17\"$ = 6Y + 50\r
\n" ); document.write( "\n" ); document.write( "Multiply through by 17\r
\n" ); document.write( "\n" ); document.write( " 17· $\"14200%2F17\"$ = 17·6Y + 17·50
\n" ); document.write( " 14200 = 102Y + 850
\n" ); document.write( " 14200 - 850 = 102Y
\n" ); document.write( " 13350 = 102Y
\n" ); document.write( " $\"13350%2F102\"$ = Y \r
\n" ); document.write( "\n" ); document.write( "That fraction reduces by dividing top and bottom
\n" ); document.write( "by 6:\r
\n" ); document.write( "\n" ); document.write( " $\"2225%2F17\"$ = Y \r
\n" ); document.write( "\n" ); document.write( "800 - 50 = 6Y
\n" ); document.write( " 750 = 6Y
\n" ); document.write( " 125 = Y \r
\n" ); document.write( "\n" ); document.write( "Substitute X = $\"14200%2F17\"$ in X = 4Z + 100\r
\n" ); document.write( "\n" ); document.write( " X = 4Z + 100
\n" ); document.write( " $\"14200%2F17\"$ = 4Z + 100\r
\n" ); document.write( "\n" ); document.write( "Multiply through by 17\r
\n" ); document.write( "\n" ); document.write( " 17· $\"14200%2F17\"$ = 17·4Z + 17·100
\n" ); document.write( " 14200 = 68Z + 1700
\n" ); document.write( " 14200 - 1700 = 68Z
\n" ); document.write( " 12500 = 68Z
\n" ); document.write( " $\"12500%2F68\"$ = Z\r
\n" ); document.write( "\n" ); document.write( "That fraction reduces by dividing top and bottom
\n" ); document.write( "by 4:\r
\n" ); document.write( "\n" ); document.write( " $\"3125%2F17\"$ = Z\r
\n" ); document.write( "\n" ); document.write( "So the solution is\r
\n" ); document.write( "\n" ); document.write( "(X, Y, Z) = ( $\"14200%2F17\"$ , $\"2225%2F17\"$ , $\"3125%2F17\"$ )\r
\n" ); document.write( "\n" ); document.write( "Are you sure your teacher asked you to solve such a
\n" ); document.write( "horrible problem with such nasty fractions? This solution
\n" ); document.write( "is correct for what you gave me. But I'll bet anything that
\n" ); document.write( "there is a sign wrong somewhere in the original problem.\r
\n" ); document.write( "\n" ); document.write( "Edwin\r
\n" ); document.write( "\n" ); document.write( " \r
\n" ); document.write( "\n" ); document.write( " \n" ); document.write( "

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