In 1950: R = 4*J         (1)

where R is Roberto's age in 1950, and J is Juan's age in 1950, at the moment of comparison. 

In 1955, 5 years later: 

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

Solve these two equations. Substitute (1) into (2) and simplify.

4J + 5 = 3J + 15,

J = 15 - 5 = 10.

So, in 1950 Juan was 10 years old. Roberto was 40 years old in 1950.

Thus Roberto is 30 years older than Juan.

Hence, Roberto was 30 years old when Juan was born.

Let Juan’s age, in 1950 be J

Then Roberto’s age, in 1950 was 4J

Therefore, difference in ages = 4J – J, or 3J

In 1955, Juan was J + 5, and Roberto was: 4J + 5

We then get: 4J + 5 = 3(J + 5)

4J + 5 = 3J + 15

4J – 3J = 15 – 5

J, or Juan’s age, in 1950, was: 10

Roberto’s age, in 1940, when Juan was born, was 3(10), or  

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