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The Problem of the First Week

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A boy is four years old and his sister is three times as old as he is. When the boy is 12 years old, how old will his sister be?

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The Solution:

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Let X be the age of the boy  => his sister's age is 3X. We know that the boy's age is 4 years => X=4 =>  the sister's age 3X=12. that was now but in the problem we need the age of the sister when the boys age is 12 years old. Easily, the difference between the ages will not change => (the sister's age when the boy's age is 4) - (the boy's age, which is 4)= 12 - 4 = 8 years. so the sister is 8 years older than the boy, so her age when the boy is 12 years old is 12 + 8= 20 20 is the right answer.

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