SOLUTION: What are five sequential numbers whose total is 63

Question 993570: What are five sequential numbers whose total is 63
Found 3 solutions by josgarithmetic, solver91311, ikleyn:
Answer by josgarithmetic(39618)   (Show Source): You can put this solution on YOUR website!
Assume x is a whole number.

, then the assumption is wrong, but we still have a result for x.

Answer by solver91311(24713)   (Show Source): You can put this solution on YOUR website!

Cannot be done. Any five consecutive integers must total to a number divisible evenly by 5. 63 is not evenly divisible by 5.

John

My calculator said it, I believe it, that settles it

Answer by ikleyn(52788)   (Show Source): You can put this solution on YOUR website!
.
It is about this problem again and again:

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Mr. X had a habit of spending money according to dates. For example, if date was 19 he was spending 19 rupees, and if date was 15 he was spending 15 rupees.
One night he calculated total spending of 5 consecutive days - Monday to Friday, and he found that he spent 63 rupees in 5 days.
So, identify the dates. (Assume that everyday spending is integer number of rupees).
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Answer. There is only one solution:
              28 and 29 of February of a leap-year and 1, 2, and 3 of March.
              (28 + 29 + 1 + 2 + 3 = 63).

Solution

If these days would be inside one month, then the dates are (x-2), (x-1), x, (x+1) and (x+2), where x is the date in the middle of 5 days.
Then the sum must be multiple of 5, since

(x-2) + (x-1) + x + (x+1) + (x+2) = 5x.

But the integer 63 is not multiple of 5. Contradiction.

Hence, the dates are partly the end of some month and the beginning of the next month.

Then, it is easy to check that the dates 28, 29, 1, 2 and 3 satisfy the condition 28 + 29 + 1 + 2 + 3 = 63.
Next, it is easy to check that there is no other solution.

The solution of this problem was placed in this forum one week ago
http://www.algebra.com/algebra/homework/word/misc/Miscellaneous_Word_Problems.faq.question.992162.html .

The solution for the similar problem was placed in the lesson Spending money according to dates in this site couple of weeks ago.

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