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1-6, pg. 152. Created by Sal Khan.
Video transcript
We're on problem 1. A project scheduled to be carried out over a single fiscal year has a budget of $12,600. Divide it into 12 equal monthly allocations. So if we divide it by 12 how much are we going to spend per month? So that's $1,050 per month. Right? 12,000 divided by 12 is 1,000. 600 divided by 12 is 50. So they're going to spend $1,050 per month. At the end of the fourth month of that fiscal year, the total amount actually spent on the project was 4,580. So 4,580 after four months. By how much was the project over its budget? Well, let's see how much they should have spent after four months. So after four months they should have spent 1,050 times 4. That's what? That's 4,000. 4 times 50. 200. That's how much they should have spent after four months if they were on budget. They ended up spending 4,580. So let's see how much they spent too much. They spent $380 too much. And that is choice A. Next question. Question 2. For which of the following values of n is 100 plus n over n not an integer? We could simplify this. This is the same thing as 100 over n plus n over n, which is equal to 100 over n plus 1. So in order for this not to be an integer-- this is the same thing. 1 is clearly an integer, so this can't be an integer, right? So we have to pick an n that is essentially not divisible into 100. So what are their choices? So they say 1. Well 100 is clearly divisible by 1. You'll get an integer there. So it's not 1. 2. 100 is clearly divisible by 2. 100 divided by 2 is 50. That's not it. 3. 100 divided by 3. That's 33.333. That's not an integer. So choice 3 will not produce an integer if it's selected for n, so we're at C. The answer is C. Next question. 3. Rectangular floors x and y have equal area. If floor x is 12 by 18-- let me draw that. This is floor x. They say it's 12 by 18. And floor y is 9 feet wide. What is the length of floor y in feet? OK, I didn't have to draw this, I think. So floor y is 9 feet wide. So they're saying it has the same area, so essentially they're saying that 9 times-- and they want to know its length. So let's call that l. So the area of floor y, which is 9l, is equal to the area of floor x, which is equal to 18 soon. times 12. And I even multiply this out, because I don't know off the top of my head what 18 times 12 is, but we can just divide both sides by 9, and we get l is equal to-- let's divide the 18 by the 9. 2 times 12, which is equal to 24. And that's choice E. Next problem. Problem 4. A case contains c cartons. Each carton contains b boxes and each box contains c-- OK, so c cartons. OK, case is equal to c cartons. Carton is equal to b boxes. And then they say a box is equal to 100 paper clips. How many paper clips are contained in 2 cases? So we could say 2 cases is equal to 2c cartons, right? So each carton has how many boxes? Has b boxes, right? So this is going to be equal to 2 times c. Right? That's how many cartons, and each carton has b boxes. So it's going to be equal to 2cb boxes. And then each of these boxes is going to have 100 paper clips, so times 100. So that is equal to 200cb paper clips. And that is choice C. They wrote bc instead of cb, but that's the same thing. So that is choice C. Next question. Question 5. The sum of prime numbers that are greater than 60, but less than 70 is? So let's just think of them. 60 is not prime so that doesn't work. 61 as far as I can tell is prime. Right? I can't think of any numbers that go into it, although maybe I'm missing a few. 62 isn't prime. That's even. 63 is 9 times 7. That's not prime. 64 is 8 times 8. 65. That's not prime, divisible by 5. 66? Nope. 67. Is 67 prime? Let's see, 67. I think it is. I can't think of any numbers that go into it. 68 is not prime. It's even. 69 is divisible by 3. And 70 is clearly not prime. So if I'm right, these are the two prime numbers. Let me make sure 61 is not divisible. It's not divisible by 3. It's not divisible by 7. Yes, 61. 17 times 3 is 51. Yes. I can't think of anything. So if we add these two numbers up, I get 128. So choice B. I hope that's right. Next question. Question 6. you A rainstorm increased the amount of water stored in state J reservoirs from 124 billion gallons to 138 billion gallons. If the storm increased the amount of water in the reservoirs to 82% of total capacity, approximately how many billion gallons of water were the reservoirs short of total capacity prior to the storm? So, let's see. How many billions prior to the storm. So this is 82% of total capacity. So capacity is going to be equal to 138 divided by 0.82, right? Well, maybe I skipped a step. Let me write that. 82% of total capacity is equal to 138. So you divide both sides by 82%, or 0.82, and you get capacity is equal to 138/0.82, right? And then they want to know how many billions of gallons of water were the reservoirs short of total capacity prior to the storm. So it's going to be this number-- this is total capacity-- minus what they were prior to the storm, 124. So we just have to do a little bit of mathematics. I don't know if they allow you to use a calculator, but I think we can do this on our own. 0.82 goes into 138. And we could take this decimal point two over, so we can move this decimal point two to the right. So we get that there. So it becomes 82 goes into 13,800 how many times. So 82 goes into 138 1 time. We get 6. 13 minus 8 is 56. 560. 82 goes into 560-- Well, let's see. 80 goes into 56 6 times. 6 times 82 is 12, plus 1. 6 times 8 is 48. 49. And then we're left with, let's see. What is that? This becomes a 5. This becomes 15. So we're left with 68. 680. 82 goes into 680 8 times. 8 times 2 is 16. 8 times 8 is 64. 65. And you're left with, I don't know, what is this? 24. 240. So after the decimal it keeps going, but the total capacity is about 168. So how short were they? 168 minus 124. So 68 minus 24 is 44 gallons. And that's choice E. They give you a little bit of hairy decimal problems. I don't know if calculators are allowed, but we did it without one. Problem 7. Actually, I'm almost of time. I'll continue this in the next video. See you soon.