Age problem

[Morris]

Hi,

I need help to solve this easy age problem. I love math but haven't done it in ages so now I have started again and it's really fun but stumbled upon this problem and not sure how to solve it as I'm not sure how to handle the 55? It probably is really easy but I'm stuck .

The problem is:
Hannah, Iris and Julie are 102 years old together. When Julie is twice as old as she is now, Hannah will be 55 years old.

 

[Dr.Peterson]

To me, the hard part is that there are two different times involved: now, and "when Julie is twice as old as she is now". (How long from now will that be?)

What I like to do is to make a table in which there is a column for each of the two times, and a row for each person. Then I can write in an expression for each cell in the table.

Once I have expressions written, I can write equations using them. With three unknown ages, I expect to see three equations.

Now, you didn't state the whole problem (only two equations, and no question), so I can't help beyond this. What I'd like to see from you is how you defined variables, and how you fill in my table (or otherwise write expressions). Then we can see what help you need.

 

[Oiler]

There is no problem here, since the question has not told you to do anything with the information given.

 

[HallsofIvy]

Hi,

I need help to solve this easy age problem. I love math but haven't done it in ages so now I have started again and it's really fun but stumbled upon this problem and not sure how to solve it as I'm not sure how to handle the 55? It probably is really easy but I'm stuck .

The problem is:
Hannah, Iris and Julie are 102 years old together. When Julie is twice as old as she is now, Hannah will be 55 years old.

"Hannah, Iris, and Julia are 102 years old together" is a strange phrasing. I would gave interpreted it as meaning that these are three women, each 102 years old!

But clearly you mean that Hannah's age, Iris' age, and Julia's age add to 102, Using "H" to mean Hannah's age, "I" to mean Iris' age, and "J" to mean Julia's age, H+ I+ J= 102. When Julia is "twice as old as she is now" she will be 2J years old which will be J years from now. Hannah's age then will be H+ J= 55.

Only two equations would not usually be not enough to solve for three unknows values but clearly the three ages are intended to be integers, the nearest exact year. Since H+ J= 55, H+ I+J= (H+ J)+ I= 55+ I= 102 so I= 102- 55= 47. There are then many different H and J that satisfy H+ J= 55. In fact, for any H, J= 55- H. We can write the general solution as H= a, I= 47, J= 55- a. Choose whatever age you like for Hanna, from 1 to 54 and Julia is 55 minus that, while Iris must be 47.