## 25 February 2008

### Frustrating (but simple) math problem

I found this on a "puzzle-a-day" calendar Christmas gift. The math required to solve it is 8th grade algebra. But it is agonizingly frustrating...

"Ellie is 33 years old. This is three times as old as Sophie was when Ellie was as old as Sophie is now."
How old is Sophie now?

Try it. Get a pencil/pen and paper (you'll need it). You'll think a sentence or some data is missing. It isn't - everything necessary to solve the question is in those two sentences.

Answer in the "comments" section. Don't peek until you sweat it out for 10 minutes.

#### 3 comments:

1. Obviously 33 is 3 times 11, which is how old "Sophie was." That's the obvious part.

Make two columns - "past" and "now."

Past - Sophie was 11, set Ellie as "x"

Now - Ellie is 33, and now (as the puzzles says), Sophie is "x."

How many years have passed between "past" and "now." You don't need to know - just know that it is the same for both girls.

So X-11 (the difference for Sophie) equals 33-X (the difference for Ellie). Rearrange, simplify, and all that, and X = 22.

2. You're making an assumption about how old Sophie was, and that the problem uses round numbers.
If you just say 33 = 3(s-x) where x is how ever many years ago this was, then we know that 33-x=s where s is the number of years old sophie is now. Then x=33-S and plug back into the first equation 33=3(s-(33-s))
33=3(2s-33)
33=6s - 99
132=6s
s=22
Your assumption happened to be correct in this case, but it isn't necessary to solve the problem.

1. I don't understand your comment about my making an "assumption about how old Sophie was..."

The problem states "...33 years old...is three times as old as Sophie was..."

And is there an answer that doesn't involve round numbers?

I understand your algebra is correct, but I don't see the error in my logic.