Thread: Fractions and algebra

Hi. I'll keep this brief and to the point.

I was teaching my sister, who's in Grade 5, math and I encountered the following problem:

Jack is 1/3 of Alex's age. In 12 years, he will be 2/3 of Alex's age. How old is Jack now?

Ans: 4 years

Of course using Algebra, I could solve it within seconds. Problem is, they do not teach Algebra in the 5th grade here, in Singapore. The standard method for solving these types of problems in Elementary school is by drawing models, based on the given fractions, then manipulating the models to find the answer. However, my knowledge of the model method is, at best, extremely rusty. I would appreciate if someone can tell me how to solve this problem without the use of algebra. Thanks!

Try to create a table and solve the problem by guessing some numbers for Jack's Age. start with a reasonable number. then find out which number will fullfill the conditions.

You could maybe use trial and error?

1/3 is not something frequently seen.
You could have:

Code:

   Now      In 12 years
Jack Alex    Jack Alex
 1    3       13   X
 2    6       14   18
 3    9       15   X
 4    12      16   24

etc.

As you can see, you can only take some specific ages (I put an X for impossible answers). Alex's age must always be a multiple of 3 now, and after 12 years while Jack's age must be even after 12 years.

And as a matter of fact, I already have an answer