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A mess of ages

A mess of ages

When we ask Maria and her little sister for their ages they answer the following: If we add three times the difference of our ages to the difference of the cubes of our ages, we get another cube as a result.

How old is Maria's sister?

Solution

Maria is 11 years old and his sister 7 since it is fulfilled that

113 - 73 = 1331 - 343 = 988

3 * (11 - 7) = 3 * 4 = 12

988 + 12 = 1000

1000 = 103