# Age word problem: I am twice as old as you were when I was y

#### the_slow1

##### New member
I got this challenge that I never figured out:

"I am twice as old as you were when I was your age. Our ages total 63. How old are we? And it's not 42 or 81"

I know the answer is 27 and 36, but I dont know why. Help, please?

#### galactus

##### Super Moderator
Staff member
Kind a rough to wrap the head around, ain't it.

y=my age now

y-x=difference in ages now

My age now is twice that.

$$\displaystyle 2(x-(y-x))=y\Rightarrow{y=\frac{4x}{3}}$$

Our combined ages is 63, x+y=63

Sub: $$\displaystyle x+\frac{4x}{3}=63$$

x=27

I hope I got that straight. :lol:

#### TchrWill

##### Full Member
Re: Age word problem

the_slow1 said:
"I am twice as old as you were when I was your age. Our ages total 63. How old are we? its not 42 or 81"
1--x = my current age
2--y = your current age
3--z = half your current age
4--x = 2(y - d)
5--x = 2y - 2d
6--x + y = 63
7--63 - y = 2y - 2d
8--3y - 2d = 63
9--Divide throug by the lowest coefficient yielding y + y/2 - d = 31 + 1/2
10--(y - 1)/2 must be an integer k making y = 2k + 1
10--Substituting back into (7) yields 6k + 3 - 2d = 63 or d = 3k - 30
11--k must be greater than 10
11--k.....11.....12....13.....14.....15
12..y.....23....25.....27......29.....31
......d.....3......6.......9.......12.....15
......x....40....38.....36......34.....32
......z....20....19.....18......17.....16

By inspection, k = 13 provides the desired answer.

#### Denis

##### Senior Member
More than one way to cat a skin:

Code:
m = me, y = you, a = years ago

m-a             m
y-a             y

........years ago..........now
m - a = y ; a = m - y [1]

m = 2(y - a) ; a = (2y - m) / 2 [2]

[1][2]: m - y = (2y - m) / 2 ; y = 3m / 4

m + y = 63
m + 3m/4 = 63
m = 36 ; y = 27