SOLUTION: find three consecutive odd numbers whose sum is 303

Question 568555: find three consecutive odd numbers whose sum is 303

Answer by bucky(2189) (Show Source): You can put this solution on YOUR website!
Consider a series of odd numbers such as 1, 3, 5, 7, 9, 11 and so on. This series consists of consecutive odd numbers because no odd number is left out. Now, notice the particular feature of this series is that each number is 2 greater than the number that comes just before it. So if 5 is the first odd number you select, the next consecutive odd number is 5 + 2 or 7. And think about this. The next consecutive number after that is two more than its predecessor, so it is 7 + 2 or 9. But 7 is equal to 5 + 2. So we can say that the third number in this series of consecutive odd numbers is (5 + 2) + 2 = 5 + 4 = 9. In fact we can write the series of consecutive odd numbers starting with 5 as (5), (5 + 2), (5 + 4), (5 + 6), (5 + 8), and so on.
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In general we can similarly write the series of odd numbers in which n represents the unknown first number, as n, n+2, n+4, n+6, n+8, ...
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So three consecutive odd numbers can be written as n, n+2, and n+4. The problem asks you to find three consecutive odd numbers whose sum is 303. You can set up the equation for the sum of three consecutive odd numbers as equal to 303 by writing it as follows:
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n + (n+2) + (n+4) = 303
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You can now simplify the left side by adding the three n terms to get 3n and then adding the 2 and the 4 to get 6. This makes the equation become:
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3n + 6 = 303
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First get rid of the 6 on the left side by subtracting 6 from both sides to simplify the equation to:
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3n = 297
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Solve for n by dividing both sides of the equation by 3 (the multiplier of x) to reduce the equation to:
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n = 99
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We identified n as the first term in the series. So the second consecutive odd term must be 2 more that 99, or it must be 101. And the third consecutive odd term must be 2 more than the second term, so it must be 103.
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Check the answer by adding 99 + 101 + 103 to ensure that the sum of these three consecutive odd numbers is 303, just as the problem requires it to be.
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In summary, the 3 consecutive odd numbers that add to a total of 303 are 99, 101, and 103.
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I hope this helps you to understand how to work problems having consecutive odd numbers.
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