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## 7th grade

### Unit 5: Lesson 6

Two-step equation word problems- Equation word problem: super yoga (1 of 2)
- Equation word problem: super yoga (2 of 2)
- Two-step equation word problem: computers
- Two-step equation word problem: garden
- Two-step equation word problem: oranges
- Interpret two-step equation word problems
- Two-step equations word problems

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# 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?

- 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.(6 votes)
- From my point of understanding. I think that Sal wants to intend 0 as an
*unknown number*that will**be replaced**by other*numbers*or*variables*in which you can leave a blank space instead of 0 if it's too confusing for you but you can never set any**variables**or**numerals**.(1 vote)

- At0:26, why did Sal wrote let? What does let mean?(3 votes)
- What he means is the total computer he sell is X(1 vote)

- i'm having trouble with this problem.

Efren leaves home at 9 a.m. and walks 4 miles per hour. His brother, Gregory leaves half an hour later and runs 8.5 miles per hour in the same direction. Predict the time at which Gregory will catch up to Efren.

I can reason that it will be just before 10 a.m because he is going over 2 x as fast as his brother but I don't exactly know how to set up the equation to find the exact answer. Thanks(2 votes)- This question requires knowledge from a more advanced area of Algebra known as Simultaneous Equations in Australia where I live, but called Systems of Equations on Khan Academy. You could learn this topic here:

https://www.khanacademy.org/math/algebra-home/algebra-basics/alg-basics-systems-of-equations

, or work from my solution which is as follows:

We know that Efren leaves home at 9 a.m. and walks 4 miles per hour in one direction. We can represent the hourly time relative to Efren's distance from home with the equation t=1/4d+9, with t representing the hourly time and d representing Efren's distance from home in miles.

Similarly Gregory leaves home at9:30a.m. and runs 8.5 miles per hour in the same direction, thereby the hourly time relative to his distance from home can be defined as t=1/8.5d+9.5. Do you agree that the time when Gregory catches up to Efren is when their distance from home is the same?

After playing around with the two equations, as I have done below:

Efren's equation-

t = 1/4d + 9

t - 9 = 1/4d

d = 4 (t - 9)

Gregory's equation-

t = 1/8.5d + 9.5

t - 9.5 = 1/8.5d

d = 8.5 (t - 9.5)

we find out that d = 4 (t - 9) = 8.5 (t - 9.5), and thus:

d = 4 (t - 9) = 8.5 (t - 9.5)

4 (t - 9) = 8.5 (t - 9.5)

4t - 36 = 8.5t - 80.75

44.75 = 4.5t

t = 9.94444444444444444444444...

And that converted into hours, minutes and seconds is9:56:20 a.m., which is the time when the two brothers would have caught up.

Hopefully I have helped!(2 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(2 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

17=x(1 vote)

- why would you multiply by 27(2 votes)
- Sum of the digits of a two-digit number is 8.

When we interchange the digits, it is found that the resulting new number is less than the original number by 54.

What is the two-digit number?(2 votes) - Wait how would you do that at4:44it says 370.3 but wouldn't you round down to 370? Why did he round up >)> Help me please.(0 votes)
- She can't sell just part of a computer. So, the answer needs to become 370 or 371. In normal situations, we would round, and you are right in that case, we would round down to 370. The key point in this problem is that she has to make $10,000 in profit. If you round down, she won't make that amount of profit. Her profit will be a little low. This is why the value was rounded up to 371 to make sure the goal of $10,000 in profit was met.

Hope this helps.(5 votes)

- Wait, but how is making $0 a profit? Shouldn't Sal have set the equation equal to at least $1?(1 vote)
- Well, technically, the problem should be set up as an inequality. 27x - 10,000 > 0

And, notice, she ends up needing to sell 370.3 computers. Since she can't sell a fraction of a computer this gets rounded up to 371. If she sells 371 computers, she will have a profit.

27(371) - 10,000 = 10,017-10,000 = 17

She has a profit of $17.(3 votes)

- All these question are years ago!(2 votes)
- No they aren't. The site defaults to showing you the top ranked questions / answers. They tend to be old. Just change the sort sequence to "recent" to the newer questions/answers.(1 vote)

## 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.