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4 times the sum of the digits of a 2 digit number is equal to the number.
\n" ); document.write( "If the digits are reversed the resulting number is 27 greater than the original number. what' s the number?
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\n" ); document.write( "Let x = 10's digit
\n" ); document.write( "Let y = units
\n" ); document.write( "then
\n" ); document.write( "10x+y = the original two digit number
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\n" ); document.write( "Write an equation for each statement:
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\n" ); document.write( "\"4 times the sum of the digits of a 2 digit number is equal to the number.\"
\n" ); document.write( "4(x+y) = 10x+y
\n" ); document.write( "4x + 4y = 10x + y
\n" ); document.write( "4y - y = 10x - 4x
\n" ); document.write( "3y = 6x
\n" ); document.write( "Simplify, divide by 3
\n" ); document.write( "y = 2x
\n" ); document.write( ":
\n" ); document.write( "\"If the digits are reversed the resulting number is 27 greater than the original number.\"
\n" ); document.write( "10y + x = 10x + y + 27
\n" ); document.write( "10y - y = 10x - x + 27
\n" ); document.write( "9y = 9x + 27
\n" ); document.write( "simplify, divide by 9
\n" ); document.write( "y = x + 3
\n" ); document.write( ":
\n" ); document.write( "From the 1st statement, replace y with 2x
\n" ); document.write( "2x = x + 3
\n" ); document.write( "2x - x = 3
\n" ); document.write( "x = 3
\n" ); document.write( "Find y
\n" ); document.write( "y = 2(3)
\n" ); document.write( "y = 6
\n" ); document.write( ":
\n" ); document.write( "Original number = 36
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\n" ); document.write( "Check solution in the statement
\n" ); document.write( "\"If the digits are reversed the resulting number is 27 greater than the original number.\"
\n" ); document.write( "63 = 36 + 27 \n" ); document.write( "