SOLUTION: 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?

Algebra.Com
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(10551)   (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:  

RELATED QUESTIONS


4 years ago i was half as old as my father. Six years hence, I will be three fifths as... (answered by josgarithmetic,greenestamps)

six years ago elliot was half as old as george. 6 years from now elliot will be... (answered by josgarithmetic,MathTherapy)

Six years ago, I was half as old as I will be four years from now. How old will I be five  (answered by jorel555)

Twp years ago, I was three times as old as I was eight years before I was half as old as... (answered by JBarnum)

How Old?
 
Eight years ago my father was three times as old as I shall be in five... (answered by Theo)

My sister is half my age.
Next year she will be three times as old as I was thirteen... (answered by chibisan)

When I was born, my father was 41 years old. Eight years ago he was three times as old as  (answered by ewatrrr)

five years ago, my grandfather was five times as old as I was. Three years from now, my... (answered by lwsshak3)

Twelve years ago my father was twice as old as I was, and three years ago our combined... (answered by ankor@dixie-net.com,josmiceli,MathTherapy)