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.
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