A girl is 6 years younger than her brother. The product of their ages is 135. Find their ages
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Let the age of the girl be a
Therefore, the age of the brother is ( a + 6 )
According to the question,
a ( a + 6 ) = 135
a^2 + 6a - 135 = 0
a^2 + 15a - 9a - 135 = 0
a ( a + 15 ) - 9 ( a + 15 ) = 0
( a + 15 ) ( a - 9 ) = 0
By zero product rule,
a + 15 = 0 OR a - 9 = 0
a = -15 OR a = 9
Therefore, the girl is 9 years old and the brother is 15 years old.
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