Question 1145983: Four years ago, I was half as old as my father. Six years hence, I will be three fifths as old as he. How old I am now?
Found 2 solutions by Theo, MathTherapy:
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! let x = your age and y = your father's age.
4 years ago, you were half as old as your father.
the formula for that is x-4 = 1/2 * (y-4)
6 years from now, you will be 3/5 as old as your father.
the formula for that is x+6 = 3/5 * (y+6)
you have two equations that need to be solved simultaneously.
they are:
x-4 = 1/2 * (y-4)
x+6 = 3/5 * (y+6)
add 4 to both sides of the first equation and subtract 6 from both sides of the second equation to get:
x = 1/2 * (y-4) + 4
x = 3/5 * (y+6) - 6
simplify both equations to get:
x = 1/2 * y - 2 + 4 = 1/2 * y + 2
x = 3/5 * y + 3/5 * 6 - 6 = 3/5 * y - 12/5
you get:
x = 1/2 * y + 2
x = 3/5 * y - 12/5
put both equations under the common denominator of 10 to get:
x = 5/10 * y + 20/10
x = 6/10 * y - 24/10
subtract the first equation from the second to get:
0 = 1/10 * y - 44/10
multiply both sides of this equation by 10 to get 0 = y - 44
add 44 to both sides of this equation and solve for y to get y = 44.
that's the current age of your father.
4 years ago, you were half the age of your father.
that means that you were half of 40 = 20.
6 years from now, you will be 3/5 * the age of your father.
your father will be 50 and you will be 3/5 * 50 = 30.
your current age has to be 24 because, 4 years ago you were 20, and 6 years from now, you will be 30.
Answer by MathTherapy(10556)  (Show Source):
You can put this solution on YOUR website! Four years ago, I was half as old as my father. Six years hence, I will be three fifths as old as he. How old I am now?
Let my age be M, and my father's, F
Then 4 years ago, F - 4 = 2(M - 4)_____F = 2M - 4
Then in 6 years' time, we get: 
5M + 30 = 3(2M + 2) ------ Multiplying by LCD, 5
5M + 30 = 6M + 6
5M - 6M = 6 - 30
- M = - 24
M, or my age is: 
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