Question 1138228: Someone please help me!!!
Three generations. Edwin, his father, and his grandfather have an average age of 53. One-half of his grandfather s age, plus one-third of his father s age, plus one-fourth of Edwin s age is 65. If 4 years ago, Edwin s grandfather was four times as old as Edwin, then how old are they all now?
I know how to do the math but I have no idea what the three equations would be... please help
Found 2 solutions by josgarithmetic, greenestamps:
Answer by josgarithmetic(39617)   (Show Source):
You can put this solution on YOUR website! ---
I know how to do the math but I have no idea what the three equations would be...
---
Literally assign variables to each of the ages, and follow the description exactly.
Answer by greenestamps(13198)  (Show Source):
You can put this solution on YOUR website!
a = Edwin
b = his father
c = his grandfather
(1) Edwin, his father, and his grandfather have an average age of 53.
(2) One-half of his grandfather's age, plus one-third of his father's age, plus one-fourth of Edwin's age is 65.
(3) 4 years ago, Edwin's grandfather was four times as old as Edwin.
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Equation (3) gives you one equation in a and c; so eliminate b between equations (1) and (2) to give you a second equation in a and c.
From (1): 
From (2): 
Subtracting: 
Substitute (3) into this last equation:
So Edwin is 24.
4 years ago, Edwin was 20; his grandfather then was 4 times as old, so he was 80. So now the grandfather's age is 80+4 = 84.
The sum of Edwin's age and his grandfather's age is 24+84 = 108, and the sum of all three ages is 159, so Edwin's father's age is 159-108 = 51.
ANSWER: Edwin is 24; his father is 51; his grandfather is 84.
To check, verify that equation (2) is satisfied:
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