Question 1145983
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.