Exercise 66

Peter, when asked by his son Junior how old he is, replies: “I am three times my son's age, and 10 years ago, we were 60 years old combined”. How old is Junior?

  1. 25

  2. 30

  3. 15

  4. 20

  5. 10

Try to solve it before checking the answer.

  1. 20

Let \( x \) be the current age of the son, which means that the current age of the father is \( 3x \).

  • Age of Junior 10 years ago:   \( x – 10 \)

  • Age of Peter 10 years ago:   \( 3x – 10 \)

Since both of their ages added up to 60, 10 years ago, we have:

\[ \begin{aligned} (x – 10) + (3x – 10) = 60 &\Rightarrow 4x – 20 = 60 \\[2em] &\Rightarrow 4x = 80 \\[2em] &\Rightarrow x = 20 \end{aligned} \]
\[ \begin{aligned} &(x – 10) + (3x – 10) = 60 \\[1em] &\hspace{4em}\Rightarrow 4x – 20 = 60 \\[2em] &\hspace{4em}\Rightarrow 4x = 80 \\[2em] &\hspace{4em}\Rightarrow x = 20 \end{aligned} \]

Hence, the age of Junior is 20 years old.

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