document.write( "Question 661156: Edwin, his father, and his grandfather have an average age of 53. One-half of his grandfathers age, plus one-third of his fathers age, plus one-fourth of edwins age is 65. If 4 years ago, edwins grandfather was four times as old as edwin, then how old are they all now?\r
\n" ); document.write( "\n" ); document.write( "I need help setting this problem up. I know how to do the math i just struggle in putting it into numbers. this is what i have so far.\r
\n" ); document.write( "\n" ); document.write( "1/2G + 1/3F + 1/4E = 65
\n" ); document.write( "E + F + G = 53
\n" ); document.write( "Am i on the right track? i think the next line is
\n" ); document.write( "4G + E = 4 Is this right? \n" ); document.write( "
Algebra.Com's Answer #411550 by Theo(13342)\"\" \"About 
You can put this solution on YOUR website!
E = edwin's age.l
\n" ); document.write( "F = edwin's father's age.
\n" ); document.write( "G = edwin's father's father's age (edwin's grandfather's age)
\n" ); document.write( "the average of their ages is (E + F + G) / 3 which is equal to 53.
\n" ); document.write( "(1/2)G + (1/3)F + (1/4)E = 65
\n" ); document.write( "solution is:
\n" ); document.write( "E = 24
\n" ); document.write( "F = 51
\n" ); document.write( "G = 84
\n" ); document.write( "you do a lot of substitutions to get the answer.
\n" ); document.write( "first thing was to remove the denominator which simplifies future calculations.
\n" ); document.write( "(E + F + G) / 3 = 53 becomes E + F + G = 159 after multiplying both sides of the equation by 3.
\n" ); document.write( "(1/2)F + (1/3)F + (1/4)E = 65 becomes 6G + 4F + 3E = 780 after multiplying both sides of the equation by 12.
\n" ); document.write( "you are given that G - 4 = 4 * (E - 4)(
\n" ); document.write( "this means that 4 years ago the grandfather was 4 times as old as the grandson.
\n" ); document.write( "from this equation, solve for G to get G = 4E - 12
\n" ); document.write( "substitute 4E - 12 for G in the equastion E + F + G = 159 to get:
\n" ); document.write( "E + F + 4E - 12 = 159
\n" ); document.write( "ombine like terms to get 5E + F - 12 = 159
\n" ); document.write( "add 12 to both sides of the equation to get 5E + F = 171
\n" ); document.write( "solve for F to get F = 171 - 5E
\n" ); document.write( "you now have:
\n" ); document.write( "G = 4E - 12
\n" ); document.write( "F = 171 - 5E
\n" ); document.write( "substitute for G and F in the equation 6G + 4F + 3E = 780 to get:
\n" ); document.write( "6 * (4E - 12) + 4 * (171 - 5E) + 3E = 780
\n" ); document.write( "simplify to get 24E - 72 + 684 - 20E + 3E = 780
\n" ); document.write( "combine like terms to get 7E + 612 = 780
\n" ); document.write( "subtract 612 from both sides of the equation to get 7E = 168
\n" ); document.write( "divide both sides of the equation by 7 to get E = 24
\n" ); document.write( "since G = 4E - 12, this means that G = 84
\n" ); document.write( "since F = 171 - 5E, this means that F = 51
\n" ); document.write( "that gets you:
\n" ); document.write( "E = 24
\n" ); document.write( "F = 51
\n" ); document.write( "G = 84
\n" ); document.write( "you then go back to the original problem and solve the original equations using those values of E, F, and G to confirm the solutions are good.
\n" ); document.write( "i did and they are.
\n" ); document.write( "you made a mistake up on top which you took the sum of their ages rather than the average of their ages.
\n" ); document.write( "even if you were perfect after that you would not have gotten the correct answer.
\n" ); document.write( " \n" ); document.write( "
\n" );