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Luanne’s age is half the sum of her brother's age and 6.
If Luanne is 9 years old, how old is her brother
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In Math, every word, every dot and even every comma does matter.
From the condition, we are given that
a) Luanne’s age is half the sum of her brothers age and 6
and
b) Luanne is 9 years old.
It means that "half the sum of her brother age and 6" is 9.
Hence, the sum of her brother age and 6 is 9*2 = 18.
It implies that her brother age is 18-6 = 12.
ANSWER. Her brother's age is 12 years.
CHECK. = = 9. ! Correct !
You may solve the problem by any way: using equations or using logical reasoning.
The movement of your thoughts is the same in both cases.