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### Course: 7th grade (Illustrative Mathematics) > Unit 6

Lesson 6: Lesson 11: Using equations to solve problems# Two-step equation word problem: computers

Learn how to construct and solve a basic linear equation to solve a word problem. Created by Sal Khan.

## Want to join the conversation?

- Hi!

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!

Pedro Carvalho

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.(71 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.(152 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.(9 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.(6 votes)

- am i the only one that never watches these videos?(4 votes)
- yes. you are.(4 votes)

- Would it be wrong if I just used division?

E.g. 10,000 / 27 ?(4 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.(4 votes)

- How do you get 0 as the profit because I thought it should be a positive or a negative(2 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)

- 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)

- tested to see if i could get it right before i watched the formula

10,000 / 27 = 370.3 (370 = x)

370 x 27 = 9990 (not >10,000)

370 + 1 = 371

371 x 27 = 10,017 (>10,000)

x = 371

same answer with much less steps(4 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)

- Are these simple to learn?(3 votes)
- Sal Khan’s voice is forever iconic in my mind(3 votes)

## Video transcript

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.