The sum of three consecutive odd numbers is 63, then find three consecutive odd numbers.
Hint: Numbers which follow each other in order, without gaps, from smallest to largest are called consecutive numbers. For example 12, 13, 14 and 15 are consecutive numbers and consecutive odd numbers differ by 2. We know that, consecutive odd number differs by 2
Complete step-by-step solution - Let the three consecutive odd numbers be x, (x + 2) and (x + 4) respectively. According to the given condition, we have x + (x + 2) + (x + 4) = 63
Open the brackets, we get
x + x + 2 + x + 4 = 63
Rearranging the terms, we get
3x + 6 = 63
3x = 63 - 6
3x = 57
Dividing both sides by 3, we get
x = 19
Therefore we can calculate the consecutive odd numbers now:
First consecutive odd number = 19
Second consecutive odd number = 19 + 2 = 21
Third consecutive odd number = 19 + 4 = 23
Note: Alternatively, three consecutive odd numbers be (2x + 1), (2x+3) and (2x + 5) respectively. Note that when numbers are in counting order, they are also in consecutive order and the sum of any two consecutive numbers is always odd.
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