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The sum of three consecutive odd numbers is 20 more than the first of these numbers. What is the middle number ?
Answer & Solution
Correct Answer:
Option
B
Let the numbers be x, (x + 2) and (x + 4)
Then,
$$\eqalign{ & \Leftrightarrow x + \left( {x + 2} \right) + \left( {x + 4} \right) = x + 20 \cr & \Leftrightarrow 2x = 14 \cr & \Leftrightarrow x = 7 \cr} $$
∴ Middle number :
= x + 2
= 9
Then,
$$\eqalign{ & \Leftrightarrow x + \left( {x + 2} \right) + \left( {x + 4} \right) = x + 20 \cr & \Leftrightarrow 2x = 14 \cr & \Leftrightarrow x = 7 \cr} $$
∴ Middle number :
= x + 2
= 9
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