From the problem, a matrix can be set up that looks kinda like this.
Jim's age Brother's age
Now 17Y X
Was Z Y
Before X Z
It should be noted that the variables X, Y, and Z were chosen randomly, as were the titles for the rows. The placement of the variables in the matrix comes from the problem.
The problem states “…when Jim was as old as is brother is now.” This shows that Jim is older (and always was) than his brother. From this we can add a third column to the matrix showing that this is the case
Jim's age Brother's age Inequality
Now 17Y X 17Y > X
Was Z Y Z > Y
Before X Z X > Z
These inequalities can be combined to form one that orders the variables:
17Y > X > Z > Y
Since Jim was born some number of years before the brother, he is always that number of years older. Thus the difference between Jim’s age at any time and his brother’s age at that time is constant. This means that the “spacing” between the terms in the long inequality is the same. This can be written as:
17Y > X > Z > Y
\__C_/ \_C_/ \_C_/
This relationship can be written algebraically like so:
17Y = Y + 3C
Solving for C:
3C = 16Y
C = 16 Y
3 This is 16/3
Assuming that Jim’s and the Brother’s ages are whole numbers (not unreasonable) the easiest solution for Y is for Y to equal 3. This causes C to equal 16 i.e. Jim was 16 when his brother was born. Similarly, if the brother was 3 at the youngest (in the above matrix), then Jim is currently 17 x 3 or 51 years old.
Using the facts that Jim was 16 when brother was born and. all of the values can be filled in the matrix. Since all of the values fit the matrix, we can say with gobs of satisfaction that Jim is currently 51 years old and his brother is currently 51 - 16 or 35 years old. This can be validated by noting that 35 + 16 (the age difference) = 51.
Incidentally, this is reasonable given that the father is currently alive, even though it wasn’t necessary to solve the problem.
Yeah, you can bring up points regarding obscure possibilities (age = 0, picnic at the gravesite, etc.) but we should be reasonable here.
tullius had the first correct answer with correct explanation. (Sorry, Protesilaus, I didn’t get your explanation.) However, this line didn’t make sense:
Jim is 51 and his brother is 35 (or Jim is 102, his brother is 70, and their father is .really old.)
only because the difference in their ages (32 years) would not fit with the rest of the matrix.
Getting a mathematical anser is fine, but it must be checked within the structure of the question.
Kudos and braggin’ rights to tullius . If you’re ever near Annapolis, MD I’ll buy the first beer.