document.write( "Question 27579: Please help me solve this.The sum of two numbers is twenty-one. Three times the smaller number is two less than twice the larger number. Find the two numbers.Thank you \n" ); document.write( "
Algebra.Com's Answer #14982 by sdmmadam@yahoo.com(530)\"\" \"About 
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): Please help me solve this.The sum of two numbers is twenty-one. Three times the smaller number is two less than twice the larger number. Find the two numbers.Thank you
\n" ); document.write( "Let the required numbers be a and b with a\n" ); document.write( "Given a + b = 21 ----(1) (the sum)
\n" ); document.write( "3 times the smaller number is 2 less than twice the larger number.
\n" ); document.write( "That is 3a is 2 less than 2b
\n" ); document.write( "That is 2b - 3a = 2 ----(2)
\n" ); document.write( "From (1), we have a = (21-b) ----(*)
\n" ); document.write( "Putting * in (2), we have
\n" ); document.write( " 2b - 3(21-b) = 2
\n" ); document.write( " 2b -63 + 3b = 2
\n" ); document.write( "(2b+3b) = 2 +63 (taking -63 to RHS, change side then change sign)
\n" ); document.write( " 5b = 65
\n" ); document.write( " b = 65/5 = 13
\n" ); document.write( "Put b = 13 in (*)
\n" ); document.write( " a + b = 21
\n" ); document.write( " a + 13 = 21 which implies a = 21-13 = 8
\n" ); document.write( "Therefore the numbers are 8 and 13.
\n" ); document.write( "Verification:
\n" ); document.write( "3 times the smaller number should be 2 less than twice the larger number.
\n" ); document.write( "That is 3a should be less than 2b by 2
\n" ); document.write( "And 3X8=24 is of course 2 less than 2X13 = 26
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