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.

Comments

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?
10:59 AM, February 20, 2009
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!
11:15 AM, February 20, 2009
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.
2:15 PM, February 23, 2009
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
2:19 AM, June 10, 2009
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