- Thread starter the_slow1
- Start date

x=your age now

y=my age now

y-x=difference in ages now

x-(y-x)=your age then

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: \(\displaystyle x+\frac{4x}{3}=63\)

I hope I got that straight. :lol:

1--x = my current agethe_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"

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.

Code:

```
m = me, y = you, a = years ago
m-a m
y-a y
........years ago..........now
```

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