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the units digits of a two-digit number is 3 more than twice the tens digit. If the digits are reversed, the new number is 9 less than 4 times the original number. Find the original number.
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\n" ); document.write( "Let x = the 10's digit
\n" ); document.write( "Let y - units digit
\n" ); document.write( "then
\n" ); document.write( "10x + y = original number
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\n" ); document.write( "Write and equation for each statement:
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\n" ); document.write( "\"the units digits of a two-digit number is 3 more than twice the tens digit.\"
\n" ); document.write( "y = 2x + 3
\n" ); document.write( ":
\n" ); document.write( "\"If the digits are reversed, the new number is 9 less than 4 times the original number.\"
\n" ); document.write( "10y + x = 4(10x+y) - 9
\n" ); document.write( "10y + x = 40x + 4y - 9
\n" ); document.write( "10y - 4y = 40x - x - 9
\n" ); document.write( "6y = 39x - 9
\n" ); document.write( ":
\n" ); document.write( " Find the original number.
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\n" ); document.write( "Substitute (2x+3) for y in the above equation:
\n" ); document.write( "6(2x+3) = 39x - 9
\n" ); document.write( "12x + 18 = 39x - 9
\n" ); document.write( "18 + 9 = 39x - 12x
\n" ); document.write( "27 = 27x
\n" ); document.write( "x = 1
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\n" ); document.write( "Then using y = 2x+3
\n" ); document.write( "y = 2(1) + 3
\n" ); document.write( "y = 5
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\n" ); document.write( "Original number = 15
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\n" ); document.write( "Check solution in the statement:
\n" ); document.write( "\"If the digits are reversed, the new number is 9 less than 4 times the original number.\"
\n" ); document.write( "51 = 4(15) - 9 \n" ); document.write( "