Welcome back, so were on problem number 5. In the schedule above, each session is to be an hour and a half. Each break is to be a quarter hour and lunch is to be one hour long. If session 4 is to end at 4:30 pm at what time should session 1 begin? So there’s actually 2 ways—just glancing this—well I just fill in this chart and actually I’m going to do that as well just to show you they get the same answer but there’s a faster way to do this problem. Essentially what they’re saying is the day ends at 4:30 right because 4:30 is the last thing that happens in the day and then there’s what time do the session 1 begins so they essentially saying what time should the day begin?
So if we can just figure out how many hours are in this day and then take that many hours from 4:30 pm, we get an answer for how when session 1 to begin. So how many hours are in the day? Well there is 1, 2, 3, 4 sessions times an hour and a half each. Well 4 x 1/2—that’s you know 6 hours you can multiply the fraction if you don’t believe me.6 hours, there is one lunch is one hour and then how many breaks are there? There is two breaks. So there’s 2 breaks times 1/4 so that equals ½.
So if were to add up the hours for the session on lunch and the breaks we would get 7 ½ hours and so then you just have to figure out what is 7 1/2 hours before 4:30 pm. And sometimes, people get uncomfortable subtracting time past noon because it gets a little weird so the way I think we have break it up Well if I go 4 ½ hours ago. If I go from 4:30 and I go minus 4 ½ hours and I get to noon. And so we all ready took out 4 ½ hours and we want to take out 7 ½ so we have three hours left to take out. So its 12, we take out 3 hours well that’s 9 and so that would be our answer. That’s the fast way to do it. Actually might not be the faster because you don’t have to think about all of these things and you’re not sure if you subtract it right. The other option is just fill it in.
The session ends at 4:30 so it has to begin at 3 an hour and a half. So that means his break will have to end at 3 o’ clock and begin it at 2:45 and—this would have to end at 2:45 and begin at 1:15, this would have to end at 1:15, begin at 12:15 and the 12:15 so if you go an hour and a half before 12:15, 2 hours will be 10:15 so it will be 10:45. This ends at 10:45 and so it’s a 50 minute break so it would have to start at 10:30 and then this ends at 10:30 and you subtract an hour and a half of that you get to 9 am which is our answer either way. So the second way, filling out actually isn’t that bad, if that immediately is what comes to you still then take too much time and you can done it that way as well.
Move on to the next problem, number 6—I’m going to change colors, number 6. If 2X - 5, X + 1 and 3X – 8 are all integers and X + 1 is a median of this integers so this is the median and what is median mean? Median mean just means a middle number right. If I have a bunch of number like 1, 3, 7, 8, 9, the middle number here is not the average its just you know what number half the number are larger and half the numbers are smaller. So in this example the middle number would be seven so that’s all median means.
So if you’re telling us that X + 1 is the median number and says which of the following can be a value for X and they give a bunch of choices. This has situation, I just try them out because these are pretty straight forward equation. They’re giving us pretty clean numbers let just try it out. Choice A, so 2X - 5 is 2 x 5 – 5 = 5, X + 1 is 5 + 1 = 6 and this is the X + 1 term so it should be our median and then 3 x 5 – 8 = 7. Well we locked out looks like the X plus took one term was the median and that’s probably a good indication that they want us to try the number because actually they gave it the first choice is being the one that work out. So the choice A, move on.
So now were on number 7, an exhibitor is selling decorative wreaths at an art and craft show. The net profit P in dollars from the sales of the wreath is given by and this is the usual piece of information. P(n) = 0.75 – 50, where n is the number of resold. How many wreaths must exhibitors sell in order to earn a net profit of a $100.00, well we want this thing to equal $100.00 right so we just said it is equal to 100, 100 = 0.75 and minus 50.add 50 to both sides 150 = 0.75 and I like to write, I like to deal with fractions. I don’t like decimal with fractions are easier, this is the same thing as we can rewrite this as 3/4 and 0.75 is the same thing as 3/4.
So now we just multiply both sides times the inverse of this coefficient so time 4/3, this of course cancels so we just have n left on the right hand side and on this hand side 4/3 times 150/1—well the 150 cancels out with the 3 right, three becomes 50, this becomes1 so 4 x 50 = 200 so one of the denominator is equal to n. There you go the exhibitor has to sell 200 wreaths which is choice E.
Problem number 8, if X² +Y² = 73 and XY = 24, what is X + Y²? What happens when you multiply out X + Y squared? X+Y² is the same thing as X plus Y times X + Y and this might be second HD after taking a lot of algebra but I’ll just multiply out just to show you. See if X times X is X², X times Y is XY, Y times X is XY and y times Y is Y². So it equals X² + 2XY + Y². Well that’s interesting, we know that these two terms combined that’s X² + Y² so we know that is equal 73. X² + 2XY + Y². So these two terms is 73 so we have 73 + right and we can cancel those two out and then we have 2XY and we know XY = 24. So it’s 2 x 24. So its 73 + 48 = I think this is going to be what? 121— lets see this is set this to 110 plus another 11, right 121. That’s all there was. You just really have to expand out X+ Y² and then you say oh well they kind of give what the component terms with the values are and then were done. I’ll see you in the next video.