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a homeowner used 200 units of electricity and 110 units of gas for a total of $79.00.
\n" ); document.write( " The next month, 230 units of electricity and 250 units of gas were used for a total of $103.20.
\n" ); document.write( " Find the cost per unit of gas.
\n" ); document.write( ":
\n" ); document.write( "x = cost per unit of electricity
\n" ); document.write( "g = cost per unit of gas
\n" ); document.write( ":
\n" ); document.write( "Substitution using decimals will involve the least work here
\n" ); document.write( ":
\n" ); document.write( "Write a cost equation for each month
\n" ); document.write( ":
\n" ); document.write( "Month one
\n" ); document.write( "200x + 110g = 79
\n" ); document.write( "200x = 79 - 110g
\n" ); document.write( "Divide both sides by 200, results
\n" ); document.write( "x = (.395 - .55g)
\n" ); document.write( ":
\n" ); document.write( "month two
\n" ); document.write( "230x + 250g = 103.20
\n" ); document.write( ":
\n" ); document.write( "replace x with (.395-.55g)
\n" ); document.write( "230(.395-.55g) + 250g = 103.2
\n" ); document.write( "90.85 - 126.5g + 250g = 103.2
\n" ); document.write( "250g - 126.5g = 103.2 - 90.85
\n" ); document.write( "123.5g = 12.35
\n" ); document.write( "g =
\n" ); document.write( "g = $.10 per unit of gas
\n" ); document.write( ":
\n" ); document.write( ":
\n" ); document.write( "In order to check our solution we have to find the cost of x
\n" ); document.write( "x = .395 - .55(.10)
\n" ); document.write( "x = .395 = .055
\n" ); document.write( "x = $.34 per unit of elec
\n" ); document.write( ":
\n" ); document.write( "Check using these values in the 2nd month equation
\n" ); document.write( "230(.34) + 250(.10) =
\n" ); document.write( "78.2 + 25 = 103.20, confirms our solution \n" ); document.write( "