QUESTION

The combined age (of he and she) is 98.

He was twice as old as she was, when he was the age she is now.

Question: What are their ages now?

SOLUTION...

So, obviously we know that

. Now, we'll make another equation for the 2nd sentence of the problem.

The right side of the equation tells us "when he was the age she is now", and the left side tells twice her age

years ago.

Now, let's substitute

the S's. This will let us solve for H. The S letters would represent her age now.

S would be 98-H.

So its

ANSWERS for their ages now

And then her age would be 39.2

So now lets check this. When he was 39.2, then she would have been 19.6.

The problem states "He was twice as old as she was, when he was the age she is now."

My answers satisfy that.

So, does it really have to be as tedious as I made it. I don't see a simpler way.

Is there some way I can solve this problem graphically?