## December 5, 2008

### Age problem

I am 5 times as old as you were when I was as old as you are.
Find our present ages.

mg said...

18 & 10

Secret SquÃ¯rrel said...

"I" am older than "you" so I > U.

When I was as old as you are now, I - T = U; where T is the time since then. I am now 5 times as old as you were back then so I = 5 * (U - T).

From I - T = U add T to both sides
=> I = U + T. Subst for I in 2nd equation
=> U + T = 5 * (U - T)
=> U + T = 5U - 5T add 5T and subtract U from both sides
=> 6T = 4U

There are an infinite number of values which satisfy these equations, but assuming that the ages and time interval are measured in whole years, the minimum that U can be is 3, with T = 2, and I = U + T = 5.

So I am now 5 and you are 3. 2 years ago I was the age you are now (3) and you were 1. I am now 5 times that age.

These values also work:
U__I__T
6 10 4
9 15 6
12 20 8
etc

Anonymous said...

I am 5 times as old as you were when I was as old as you are.

age is i=5X, u=X

i am five times as old as u.I=5U

Beca said...