document.write( "Question 3478: The difference between two numbers is 12. If 2 is added to seven times the smaller number, the result is the same as if 2 is subtracted from three times the larger number. Find the numbers. \n" ); document.write( "

Algebra.Com's Answer #1551 by Pieter(35) $\"\"$ $\"About$

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the difficulty of this exercise is to transform the text ito symbols.\r
\n" ); document.write( "\n" ); document.write( "The difference between two numbers is 12: a-b = 12 (I)
\n" ); document.write( "(then we choose a the largest number and b the smallest\r
\n" ); document.write( "\n" ); document.write( "If 2 is added to seven times the smaller number, the result is the same as if 2 is subtracted from three times the larger number: this becomes:
\n" ); document.write( "7b+2 = 3a-2 (II)\r
\n" ); document.write( "\n" ); document.write( "from (I) we get: a = 12+b and this we fill in into (II), this method is called 'substituting' because you change a part in one equation with information you get from another one. So we get:\r
\n" ); document.write( "\n" ); document.write( "7b+2 = 3(12+b)-2
\n" ); document.write( "7b+2 = 36+3b-2
\n" ); document.write( "7b-3b = 36-2-2
\n" ); document.write( "4b=32 or b=32/4= 8\r
\n" ); document.write( "\n" ); document.write( "and we know a = 12+b = 12+8 = 20\r
\n" ); document.write( "\n" ); document.write( "check: 20-8=12 (I) ==>ok
\n" ); document.write( " 2+7*8 = 3*20-2 ==>ok\r
\n" ); document.write( "\n" ); document.write( "Contact me if you have any questions \n" ); document.write( "

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