Question 992526: One person had a habit of spending money according to dates.one night He calculated total spending of five consecutive days. Monday to Friday and he found that he spent rupees 63 in five days. Identify dates
Found 2 solutions by stanbon, ikleyn:
Answer by stanbon(75887)   (Show Source):
You can put this solution on YOUR website! One person had a habit of spending money according to dates.one night He calculated total spending of five consecutive days. Monday to Friday and he found that he spent rupees 63 in five days. Identify dates
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1st date:: x
2nd date:: x+1
3rd date;; x+2
4th date:: x+3
5th date:: x+4
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Sum = 63
5x + 10 = 63
5x = 43
x = 8.6
That doesn't make any sense.
The value must be a whole number.
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Cheers,
Stan H.
Answer by ikleyn(52834)  (Show Source):
You can put this solution on YOUR website! .
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.
This problem was just offered and solved in this forum one-two weeks ago (# 990684, the link
http://www.algebra.com/algebra/homework/word/misc/Miscellaneous_Word_Problems.faq.question.990684.html ).
The problem and the solution were also placed in the lesson Spending money according to dates in this site.
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