a. There are 365 days per year, 24 hours per day, 12 months per year, and 60 minutes per hour. Use these data to determine how many minutes are in a month. b. Now use the following data to calculate the number of minutes in a month: 24 hours per day, 60 minutes per hour, 7 days per week, and 4 weeks per month. c. Why are these answers different? Which (if any) is more correct? Why?
All right. So let's try to figure out how many minutes there are in a month. And so we can only use the conversion factors that were given in the problem and we want to eventually get two minutes per month. So we're given several conversion factors were given the fact that there's 365 days per year. were given the fact that there's 24 hours in a day and we don't want days in our answer. So we're going to put days in the bottom. I want to put the hours then in the top 24 hours in a day. And so the days will go away. But we have hours and years. We don't have minutes and months. So we have to keep going. There are 12 months in a year. I need years to cancel. So I'm gonna put the year in the numerator, one year is 12 months. Okay. And so the year and the year will cancel out. Now I have months where I want it in the denominator And finally we're told there was 60 minutes in an hour and I am going to put the hours on the bottom because I needed to cancel out with the hours on the top and now I have minutes in the numerator months and denominator. That's what I'm looking for. So now I know that I can go and solve and so there are 7800 minutes in a month using these sets of equalities. But we could also go about it in a different way. So we can still look for minutes in a month but with a different set of conversion factors. Uh huh. And so let's say we know that there are 24 hours in a day And we know that there is 60 minutes in an hour. So the hours cancel out. We know that there's seven days in a week. Now I'm putting days uh in the numerator so I can cancel the days out that were in the denominator and four weeks in a month. And so the week's cancel out, we're left with minutes over months. So we know that we can solve And we wind up with 40,000 320 minutes in a month. And I went back and I saw gee how could these two numbers be so drastically different And they can't. And so when I originally typed in the calculator here, I put in 65 instead of 3 65. So when I went back and I did the math again, What I found was that this is actually 43,000 800. All right, so between the two of these, then um like why are these different? And which one is the better one? I would say that a Is the better one. And the reason I would say that a is the better one is based on four weeks Per month. And that might be good in February most of the time where there's 28 days or four weeks But we have 30 days and 31 days in most of our months. And so we don't have four weeks. We actually have more than four weeks. So I would say that a is better based on most months, four weeks Does't Equal one Month.