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MathNet 2006 — Part 02 Question 20

Math Olympiad Vault · MathNet 2006 — Part 02

Question 20

Mr. José has four grandchildren, all of different ages. The age difference between the oldest and youngest grandchildren is $6$ years and the age difference between the other two grandchildren is $1$ years. One of the four grandchildren is $12$ years old. It is known that, by making two parallel cuts on the sides, as shown in the figure, Mr. José can split a rectangular bar of chocolate into four parts whose areas coincide with the ages of the four grandchildren.
How old are Mr. José's grandchildren?

Question illustration