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Question 98168: What are the five odd numbers that their sum is equal to fifty?
Answer by jgr45(31)   (Show Source):
You can put this solution on YOUR website! This problem is so easy one could do it in their head if s/he uses the right method. Most people would set x = to the smallest number, but I prefer to set x = to the middle number instead.
Here we are asked to find five odd numbers; therefore the difference between each number will be 2. If x = the middle number, then
first number = x-4
second number = x-2
third number = x
fourth number = x+2
fifth number = x+4
And we are told that the sum = 50.
(x+x+x+x+x) + (-2+2) + (-4+4) = 50
5x = 50 (see how handy setting x=middle # can be?) :)
x = 10
The numbers that sum to 50 are 6, 8, 10, 12, and 14.
However, the problem says 5 ODD numbers. Since these numbers are not odd, there is NO SOLUTION. Had the problem said to find three consecutive EVEN numbers, the solution would be the above numbers; and absent any restrictions on odd/even, the numbers would be 8, 9, 10, 11, and 12.
Whenever you are asked to find an odd number of consecutive integers (usually 3 or 5), a good trick is to set your variable to the middle number and in your equation you will be left with simply your variable multiplied by the number of consecutive numbers you are being asked to find equaling the total.
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