A little algebra problem

Just to "flex your algebra muscles" a bit; it's not too hard:
Raju is 19 years younger than Ram.  After 5 years, their ages will be in the ratio of 2:3. Find their present ages.

Solution:

Let Raju's age be J and Ram's age be R. We can make two equations:

J + 19 = R (Raju is 19 years younger than Ram)

 J + 5 R + 5 = 2 3 (The ratio of (Raju's age in 5 years) to (Ram's age in five years) is 2/3.)

We will cross-multiply the latter equation:

3(J + 5) = 2(R + 5)

At this point, one can either resolve the parenthesis, or substitute from the first equation R = J + 19 in R's place. It won't matter which you do. I'll substitute R = J + 19.

3(J + 5) = 2(J + 19 + 5) Now, add 19 + 5.

3(J + 5) = 2(J + 24) Then use distributive property.

3J + 15 = 2J + 48

J = 33.

Then check: If Raju is now 33 and Ram is 52, then in five years they will be 38 and 57. And, 38/57 = 2/3. So yes, it checks. Anonymous said…
This is the sort of problem that I always used to have to solve with algebra. But my son, who grew up with Singapore math diagrams, snorts at it and calls it "easy" -- and does it in his head!

Don't you love it when the student surpasses the teacher? Maria Miller said…
I have to admit I like algebra better, probably because I'm so used to it.

It IS an easy problem, but it's great if you can do it in your head! Anonymous said…
Mental math method: The difference between the ages will always be 19 years. Think of the ratio 2:3 in terms of a bar diagram or other visual representation, so the difference in their ages is one unit.

If one unit is 19, then the ages would be 2x19=38 and 3x19=57. But that is 5 years in the future, so we subtract 5 to get the present ages. Simon Jensen said…
Here is another type of problem:

http://blogoff.simonjensen.com/#post0

And yet another:

http://blogoff.simonjensen.com/#post4

Best wishes,
Simon