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Two-step equation word problem: oranges

Learn how to solve a word problem by writing an equation to model the situation. In this video, we use the linear equation 210(t-5) = 41,790. Created by Sal Khan.

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  • male robot donald style avatar for user Ryan Merritt
    Whoa, how does Sal do that complex division using MENTAL MATH? Can someone tell me his strategy of doing math that easily?
    (71 votes)
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  • leaf green style avatar for user wjspeicher
    wait so how is 41,970 divided by 210 the same as 42,840 divided by 210
    (9 votes)
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  • blobby green style avatar for user gamer math girl
    this is not that easy than i was thinking how to they to it?
    (6 votes)
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  • blobby green style avatar for user Lashanda
    How to determine which operation to use??

    I know how to slove but dont know how to set the word problem up have a bad struggle in that,
    (3 votes)
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  • blobby green style avatar for user Zahraa
    I am confused with this video. In class I didn't get what my teacher was saying so I thought this would help me I searched for this abt the same question in class but after all I'd rather continue in school than watch this again.
    Someone repeat this question in an easier way to understand!!
    Thanks if u can help
    (3 votes)
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  • leaf grey style avatar for user Dyre
    I kind of need some help here. I'm having trouble evaluating the two-step equations the way Kahn wants me to and it's marking me wrong whenever I evaluate it differently. I try to do it the way Kahn wants but it's so confusing and I don't get it.
    Also why is it marking me wrong when my answer is correct, but it's just my formula that's different? Can't there be more than one acceptable way of evaluating things if the answer is still correct?

    I talked to my mom and she says it seems correct to her so I should report it as a problem, so I did. But now I feel bad because the problem is with me and not Kahn. Kahn explains it but I just don't get it that way.

    Please help!
    (2 votes)
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    • mr pink green style avatar for user David Severin
      At least on the final two step equations word problems, the answer that you do have to get both the question and answer correct to get the question right. One issue that could cause problems is that you are not using the variable that they ask you to use. I found this out when I got the correct equation, but used x instead of q. While you could possibly have multiple ways of analyzing these word problems, the practice requires a two (or possibly 3 step equation if you have parentheses and you distribute first) step equation, so if you are trying to write it as a one-step equation, it will be wrong.
      I was able to get numerous questions correct, but I have many years of math behind me.
      The only way to find if your equations look good is to state a specific problem (I remember the orange tree problem, the number of test questions, and the cake problems).
      (2 votes)
  • piceratops tree style avatar for user ProGamer
    How does he make his writing so neat on a computer with a mouse?
    (2 votes)
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  • blobby green style avatar for user Danny Winters
    How do you know when to put parentheses? If you don't use them the answer is wrong..
    (1 vote)
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    • stelly yellow style avatar for user A Step Ahead From Math 🎒
      Use parentheses around nonessential information or abrupt changes in thought. ...
      If the information in parentheses requires a question mark or an exclamation mark, use the mark inside the parentheses only if the sentence ends with a different mark. ...
      Use parentheses to clarify preceding words. ...
      Use parentheses for references or documentation of sources
      (0 votes)
  • cacteye green style avatar for user yes
    how does he write SO perfectly on the computer?
    (1 vote)
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  • aqualine ultimate style avatar for user Reg
    I'm still confused with this
    (2 votes)
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    • duskpin tree style avatar for user Caleb Taylor
      We have to find the number of trees on McDonald's farm originally. Whatever you do on one side of the equation you have to do on the other side. So Sal is performing an operation on the side with the variable and also on the other side, for equality. For example: t-5 can be cancelled out by ADDING 5 to BOTH sides. Eventually, all that will be left is the variable on one side and a number on the other side. This is your solution.
      (0 votes)

Video transcript

MacDonald had a farm with a certain number of orange trees. He had to cut down 5 trees to control the insects. Each of the remaining trees produced 210 oranges, producing a total harvest of 41,790 oranges. How many trees did MacDonald's farm have initially? Let's let t equal what they're asking is for. So this is the number of trees initially. So he starts off with t trees, but then they tell us that he has to cut down 5 trees to control the insects. So how many trees would he have after that? Well, he started with t, and he had to cut down 5, so he's going to have t minus 5 trees now. Now, they tell us that each of the remaining trees-- and we know there are t minus 5 remaining trees-- produced 210 oranges. So each of these t minus 5 trees are going to produce 210 oranges. So this is the number of oranges that t minus 5 trees are going to produce. This is the number of trees times the oranges per tree. So this is the total number of oranges produced after cutting the 5 trees. And then they tell us that this ends up being a total harvest of 41,790. So this is equal to 41,790. So we've set up our equation. Now we just have to solve for t, the number of trees that MacDonald initially had. So the first thing I would do here is, well, I'm multiplying this expression by 210. Well, why don't I just divide both sides of this by 210? There's many ways that you could do this. You could distribute the 210 and go in another direction. Actually, I will do it both ways just to show that you could do it both ways. So the first way, I'm going to divide both sides by 210. The left-hand side simplifies to t minus 5. The right-hand side-- let's see, what is 4,000-- I'm going to do some long division here. I'll do it on the side, so 41,790 divided by 210. Let's see, 210 does not go into 4. It does not going into 41. It goes into 417 one time, because two times would be 420-- one time. 1 times 210 is 210. You subtract. You get 207, and then you bring down the 9. How many times does 210 go into 2,079? It looks like it would go into it not quite 10 times. It looks like it would go into it nine times. 9 times 210 is going to be-- let's see. 9 times 0 is 0. 9 times 1 is 9. 9 times 2 is 18. And then we subtract again. 9 minus 0 is 9. We have to regroup from the thousands place, so let's take 1,000 from there. Let's give that 1,000 to the hundreds place, so it becomes 10 hundreds. But then we have to take 100 from the hundreds place, so this becomes 9, and give to the tens place. So this becomes 17 tens, or 170. So 17 minus 9 is 8. 9 minus 8 is 1. So we get 189. And now we can bring down another 0. It's a little off-center right now. And we already see that 210 goes into 1,800 ninety-nine times. 9 times 210 is 1,890. When we subtract, we have no remainder. So what we get on the right-hand side is 199. And now we just have to add 5 to both sides. Remember, whatever we have to do to one side, we have to do the other. Otherwise, the equality wouldn't be equal anymore. They were equal before adding 5, so if you want them to still be equal, you have to do the same thing to both sides. So the left-hand side becomes t. I'll do the t in that purple color. And the right-hand side becomes 204. So he started off with 204 trees. Now, I told you there's multiple ways to do this. Instead of dividing both sides by 210, you could have decided to distribute the 210. And then you would have ended up with-- let me do another alternate way of doing it. 210 times t minus 5 times 210. Actually, let me just multiply it out so we save some space. 5 times 210 is 1,050-- minus 1,050 is equal to 41,790. And then you could add 1,050 to both sides. And so let me do that, 1,050 to both sides. 1,050, not 150. The left-hand side, you're just going to be left with 210t. While the right-hand side, let's see, you're going to be 0 plus 0 is 0. 9 plus 5 is 14. 1 plus 7 is 8-- 42,840. And now you can divide both sides by 210. Now we know where this is going to go. I could do the long division again. t is going to be equal to 42,840 divided 210, which is equal to 204.