document.write( "Question 27685: The sum of 3 times Gary's age and 5 times Tom's age is 150. Tom is 9 years less than twice as old as Gary is. How old is Tom?
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Algebra.Com's Answer #15078 by sdmmadam@yahoo.com(530)\"\" \"About 
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The sum of 3 times Gary's age and 5 times Tom's age is 150. Tom is 9 years less than twice as old as Gary is. How old is Tom?\r
\n" ); document.write( "\n" ); document.write( "Let Gary's age be G years
\n" ); document.write( "and Tom's age be T years.
\n" ); document.write( "Given the sum of 3times Gary's age and 5 times Tom's age is 150
\n" ); document.write( "The sum of 3G and 5T is 150
\n" ); document.write( "That is 3G + 5T = 150 ----(1)
\n" ); document.write( "Tom is 9 years less than twice as old as Gary is.
\n" ); document.write( "T is 9 less than 2G
\n" ); document.write( "That is 2G is greater than T by 9
\n" ); document.write( "That is 2G - T = 9 ----(2)
\n" ); document.write( "(1) and (2) art two equations in the two variables T and G.
\n" ); document.write( "Observe the equations.
\n" ); document.write( "If we multiply (2) through out by 5 (to equalise the coefficients of T)and add the resulting equation with (1)thereby getting rid of T and we will arrive at a single equation in the single variable G.
\n" ); document.write( "Therefore (2) X5 gives
\n" ); document.write( " 10G - 5T = 45 ----(3)
\n" ); document.write( " 3G + 5T = 150 ----(1)
\n" ); document.write( "(3) + (1) implies
\n" ); document.write( " 13G = 195 (learn to add vertically being careful with the signs instead of showing the work of adding left with the left and right with the right and then simplifying!)
\n" ); document.write( "G = 195/13 = 13X15/13 = 15
\n" ); document.write( "Put G = 15 in (1)
\n" ); document.write( "3G + 5T =150
\n" ); document.write( "3X15 + 5T = 150
\n" ); document.write( "45 + 5T = 150
\n" ); document.write( "5T = 150-45
\n" ); document.write( "5T = 105
\n" ); document.write( "T = 105/5 = 5X21/5 = 21
\n" ); document.write( "Therefore Tom is 21 years old.
\n" ); document.write( "Verification: Since we have put one value in equation (1) to find the other value, we use the other equation (2) for verificaiton.
\n" ); document.write( "(2)is 2G - T = 9 ----(2)
\n" ); document.write( "LHS = 2G - T = 2X15 - 21 = 30-21=9 = RHS which is correct
\n" ); document.write( "Tom should be 9 years less than twice as old as Gary is.
\n" ); document.write( "Of course Tom's age 21 years is 9 less than 30 = twice Gary's age as Gary's age is 15 years \r
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