Counting Days of the Week
Date: 02/02/99 at 22:26:08 From: Joel Subject: Math If today is Thursday, what day would it be 120 days from now? I have figured it using different months to start and then counting to 120 days. I feel the answer could be different each time depending on the number of days in each month. I sure would like to figure out this problem mathematically. Thank you.
Date: 02/03/99 at 11:16:28 From: Doctor Erin Subject: Re: Math Hi Joel! This is an interesting problem. I understand why you think that the answer might depend on the number of days in the month. Whether this is true depends on what exactly the question means. If "what day it would be" means what date it would be, like the 13th or the 22nd, then it certainly would depend on the months. However, if we assume "what day would it be" means what day of the week, like Monday or Friday, then the month (the number of days in the month) does not matter. For example: if the 28th of October is a Wednesday, 9 days later would be the 6th of November, which is a Friday. In the same way, if the 28th of April is a Wednesday, 9 days after that is the 7th of May, which is also a Friday. This shows you that the number date depends on the month, but the day of the week doesn't, even though April and October have different numbers of days. We know that nine days after any Wednesday will be a Friday. Try a few more examples to make sure you understand how this works. You were right, though; there is an easier way to do this problem than counting: Think about any Thursday. How many days is it until the next Thursday? I hope you got seven. Now, seven more days is a Thursday again. Check this out several more times. You will see that 7 days, 14 days, 21 days, ... after the first Thursday are all Thursdays as well! All we are doing here is counting by weeks at a time instead of days. Notice that 14 = 7*2, 21 = 7*3, and this continues for 7*4, 7*5, etc. So, if we want to find what day of the week it will be 120 days after a Thursday, we can simplify this by "counting" the Thursdays (or weeks) between the original one and the day we are looking for. We would do this by dividing the number of days we are counting by 7 to find the number of weeks, and then using the remainder to count to the day we are looking for. I will solve a similar problem to make sure you are on the right track for your question. For example, if we wanted to find what day of the week it would be 45 days after a Tuesday, this is how we would do it: 45/7 = 6 (remainder 3) This means we are counting 6 weeks and 3 days from the Tuesday. Six weeks from the Tuesday will still be a Tuesday, and if we count forward three extra days, we find that it is a Friday. Now we know that 45 days after any Tuesday is a Friday. You can use this example to find out what day it will be 120 days after any Thursday. Good luck Joel, and write back if you have any questions. - Doctor Erin, The Math Forum http://mathforum.org/dr.math/
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