Thread: Word Problem

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?

Originally Posted by SteveC

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?

Your solution strikes me as good as any.

You might simplify the algebra a bit by setting X = H-S giving your three equations in three unknowns. It is pretty simple to eliminate the X to get H = 3/2 S and that is basically what you did anyway.

You could try linear combinations, although the level the level of tediousness of the problem wouldn't change much.