Algebra (all content)
Learn how to construct and solve a basic linear equation to solve a word problem. Created by Sal Khan.
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Why do we round the number ''370.3'' to ''371''?
While I do understand that 0.3 isn't a whole computer - and that Sal wants to determine the minimum number of computers Marcia needs to sell in order to make a profit -, I don't get why we should round numbers up.
The reason I ask is because, a few minutes ago, I made an exercise that told me that 22.25 months should be rounded to 23 months! Isn't the decimal too low to make the digit to the left of the decimal point go up?
Sorry if I wasn't able to explain myself better. Thanks in advance!
PS: The problem that told me to round 22.25 up to 23 is from Khan Academy. It is from the Linear Equation Word Problems.(67 votes)
- There's a difference between rounding a number to the nearest integer (in which case 370.3 would become 370 and 22.25 would become 22) and rounding up a number, which we do when we want to know the smallest integer that solves a problem. Here, 370.3 would be the smallest number of computers that would allow Marcia to make a profit. But she cannot sell 0.3 computers, so we need to find the smallest integer that solves the problem. 370 won't do, because it is smaller than the smallest number that allows a profit -- so selling 370 won't make a profit. So we need to round UP to the next integer higher, which is the smallest integer that solves the problem.(143 votes)
- How is $0 a profit? Profit is defined as a "financial gain"- google dictionary. So, how is zero a gain? I understand that at the end of the video the final answer was 371, but his original intention was to find out the amount of computers she needs to sell to make zero dollars.(7 votes)
- It makes sense to first find the number of computers that need to be sold in order to break even (no gain and no loss), so that we can then find the minimum number of computers that need to be sold to make a profit.
Money is gained per computer sold. So any number of computers sold that is more than the number needed to break even does make a financial gain. Note that in the end, the number of computers that need to be sold to break even is a decimal. When this is rounded up to the next integer, this integer number of computers sold does result in a financial gain.(5 votes)
- How do you get 0 as the profit because I thought it should be a positive or a negative(3 votes)
- Profit = Earnings - expenses.
As such, profit can be negative (a loss); positive (you actually made money); or 0 you earned nothing.
If you earn enough money to cover your expenses but no extra, then you have 0 profit.(7 votes)
- Would it be wrong if I just used division?
E.g. 10,000 / 27 ?(3 votes)
- That is what Sal eventually got to doing. While that answers the question, Marie may want to ask different profit questions, breaking even will not make a business viable. Plus, this does not sound like a very good business to be in.(3 votes)
- can't this just be a simple division question, 10000 divided by 27?(2 votes)
- Yes which is what he ends up doing, but there is also value in trying to translate word problems into Math symbols because it may not always be that simple(5 votes)
- What is really frustrating is that you can just do this problem by dividing 10,000 divided by 27, and you get your answer. Why isn't the problem something you can only answer using this method?(4 votes)
- I am having the same problem. Like the forest in the trees, I see how it can be completed and loose sight of the methodology they are trying to teach.
Does anyone have a good resource for word problems? I have actually considered just failing that part of the class, but I know I can't do that. Any input on word problems? Mahalo peter(1 vote)
- To answer people who question the rounding 370.3 to 371, Sal just wants to make sure it's accurate, because honestly, you can't sell 370.3 computers. That would make no sense.(3 votes)
- I have really hard questions for homework like "Find a number that is 68 greater than three times its opposite" ...I honestly don't get any of this.(3 votes)
- It says it has to be 68 greater so that means 68 is added to it. Then 3 times means the number is multiplied by 3, the opposite part is the confusing part. The opposite of a positive is negative, and opposite of negative number is positive. So supposing the number is positive, then the 3 is multiplied by a negative number. This is what I think it looks like.
68-3x=x Add 3x to both sides
68=4x Divide by 4
- Why is she selling computers for 27$(2 votes)
- $27 is her PROFIT from selling a computer. For example she could've bought computers for $1000 per computer and sold them for $1027 per computer. Thus her profit is $27.(2 votes)
- Why did Sal switch sides2:28(the variable and the number)(2 votes)
- He switched the sides simply because it's customary to write equations with the variable on the left and the number on the right. Switching the sides doesn't change the validity of the equation. For example, if 2 + 7 = 13 - 4, then 13 -4 = 2 + 7.(2 votes)
Marcia has just opened her new computer store. She makes $27 on every computer she sells and her monthly expenses are $10,000. What is the minimum number of computer she needs to sell in a month to make a profit? So I'll let you think about that for a second. Well, let's think about what we have to figure out. We have to figure out the minimum number of computers she needs to sell. So let's set that to a variable or set a variable to represent that. So let's let x equal the number of computers she sells. Number of computers sold. Now, let's think about how much net profit she will make in a month. And that's what we're thinking about. How many computers, the minimum number she needs to sell in order to make a net profit? So I'll write her profit is going to be how much money she brings in from selling the computers. And she makes $27 on every computer she sells. So her profit is going to be $27 times the number of computer she sells. She gets $27 per computer times the number she sells. But we're not done yet. She still has expenses of $10,000 per month. So we're going to have to subtract out the $10,000. What we care about is making a profit. We want this number right over here to be greater than 0. So let's just think about what number of computers would get us to 0. And then, maybe she needs to sell a little bit more than that. So let's see what gets her to break even. So break even-- that's 0 profit. Neither positive or negative-- is equal to 27 times-- and I'll do it all in one color now. 27x minus 10,000. Well, we've seen equations like this before. We can add 10,000 to both sides. Add 10,000 to both sides, so it's no longer on the right-hand side. And we are left with 10,000. 10,000 is equal to 27x. And then to solve for x, we just have to divide both sides by 27. Let's do that. Divide both sides by 27. On our right-hand side, we have x. So let me just write this down. So we have x on our right-hand side is going to be equal to 10,000/27. I switched the right and the left-hand sides here. Now, what is this going to be? Well, we can do a little bit of long division to handle that. So 27 goes into 10,000. So 27 doesn't go into 1. Doesn't go into 10. It goes into 100 three times. 3 times 27 is what? 81. 100 minus 81 is 19. Then we can bring down a 0. 27 goes into 190? It looks like it will go into it about six times. Let's see if that's right. 6 times 7 is 42. 6 times 2 is 12. Plus 4. 16. Let's see, 90 minus 62 is actually 28. Let me turn this back. So it goes 7 times. 7 times 7 is 49. 7 times 2 is 14. Plus 4 is 18. There you go. Look at that. So 190 minus 189. We get 1. Let's bring down another 0. We bring down another 0. We have a 0 right there. 27 goes into 10 how many times? Well, it doesn't go into 10 at all. So we'll put a 0 right there. 0 times 27 is 0. Then we subtract. And then, we get 10 again. And now we're in the decimal range. Or we're going to start getting decimal values. We can bring down another 0. We could get 27 goes into 100 three times. So our x-value is going to be approximately 370.3. And then we're going to keep going on and on and on and on. But this is enough information for us to answer our question. What is the minimum number of computers she needs to sell in a month to make a profit? Well, she can't sell a decimal number of computers, a third of a computer. She could either sell 370 computers. If she sells 370 computers, then she's not going to get to break even because that's less than the quantity she needs for break even. So she needs to sell 371. She needs to sell 371 computers in a month to make a profit.