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?
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.
1/2G + 1/3F + 1/4E = 65
E + F + G = 53
Am i on the right track? i think the next line is
4G + E = 4 Is this right?
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! E = edwin's age.l
F = edwin's father's age.
G = edwin's father's father's age (edwin's grandfather's age)
the average of their ages is (E + F + G) / 3 which is equal to 53.
(1/2)G + (1/3)F + (1/4)E = 65
solution is:
E = 24
F = 51
G = 84
you do a lot of substitutions to get the answer.
first thing was to remove the denominator which simplifies future calculations.
(E + F + G) / 3 = 53 becomes E + F + G = 159 after multiplying both sides of the equation by 3.
(1/2)F + (1/3)F + (1/4)E = 65 becomes 6G + 4F + 3E = 780 after multiplying both sides of the equation by 12.
you are given that G - 4 = 4 * (E - 4)(
this means that 4 years ago the grandfather was 4 times as old as the grandson.
from this equation, solve for G to get G = 4E - 12
substitute 4E - 12 for G in the equastion E + F + G = 159 to get:
E + F + 4E - 12 = 159
ombine like terms to get 5E + F - 12 = 159
add 12 to both sides of the equation to get 5E + F = 171
solve for F to get F = 171 - 5E
you now have:
G = 4E - 12
F = 171 - 5E
substitute for G and F in the equation 6G + 4F + 3E = 780 to get:
6 * (4E - 12) + 4 * (171 - 5E) + 3E = 780
simplify to get 24E - 72 + 684 - 20E + 3E = 780
combine like terms to get 7E + 612 = 780
subtract 612 from both sides of the equation to get 7E = 168
divide both sides of the equation by 7 to get E = 24
since G = 4E - 12, this means that G = 84
since F = 171 - 5E, this means that F = 51
that gets you:
E = 24
F = 51
G = 84
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.
i did and they are.
you made a mistake up on top which you took the sum of their ages rather than the average of their ages.
even if you were perfect after that you would not have gotten the correct answer.
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