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2-step word problem: theater

Solve a two-step word problem by drawing a picture and creating an equation. Created by Sal Khan.

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  • mr pants teal style avatar for user Wrath Of Academy
    What if they removed 2 seats per row instead?
    (22 votes)
  • hopper cool style avatar for user Siddharth Muthyala
    isn't nine times nine 81?
    (5 votes)
  • duskpin sapling style avatar for user ANAIAH WILSON
    How would you explain the problem easily for someone who is just starting this?
    (1 vote)
    • leaf green style avatar for user Chris Tollefson
      There's a theater, which already has a certain number of seats; and they are going to install some more new seats, so that more people can sit and watch the plays or concerts in the theater. We have to figure out how many total seats there will be altogether, after they've installed the new seats.

      Here are some of the things they tell us about it:
      - There are already 63 existing seats (before the installation of new seats).
      - There are 9 rows of seats.
      - They are going to add 2 new seats to each row.

      So, before installing any new seats, here are the 63 existing seats they've already got in the theater. Each dot represents one seat:
      ┌───────┐
      Row 1: │•••••••│
      Row 2: │•••••••│
      Row 3: │•••••••│
      Row 4: │•••••••│
      Row 5: │•••••••│
      Row 6: │•••••••│
      Row 7: │•••••••│
      Row 8: │•••••••│
      Row 9: │•••••••│
      └───────┘
      63
      existing
      seats

      For each of the 9 rows, they are going to add 2 new seats:
      ┌───────┐ ┌──┐
      Row 1: │•••••••│ + │••│
      Row 2: │•••••••│ + │••│
      Row 3: │•••••••│ + │••│
      Row 4: │•••••••│ + │••│
      Row 5: │•••••••│ + │••│
      Row 6: │•••••••│ + │••│
      Row 7: │•••••••│ + │••│
      Row 8: │•••••••│ + │••│
      Row 9: │•••••••│ + │••│
      └───────┘ └──┘
      63 + ?
      existing new
      seats seats

      So they are going to add some number of new seats to the 63 existing seats. And after they do that, they will then have some new number of total seats altogether:
      ┌───────┐ ┌──┐ ┌───────┬──┐
      Row 1: │•••••••│ + │••│ = │•••••••│••│
      Row 2: │•••••••│ + │••│ = │•••••••│••│
      Row 3: │•••••••│ + │••│ = │•••••••│••│
      Row 4: │•••••••│ + │••│ = │•••••••│••│
      Row 5: │•••••••│ + │••│ = │•••••••│••│
      Row 6: │•••••••│ + │••│ = │•••••••│••│
      Row 7: │•••••••│ + │••│ = │•••••••│••│
      Row 8: │•••••••│ + │••│ = │•••••••│••│
      Row 9: │•••••••│ + │••│ = │•••••••│••│
      └───────┘ └──┘ └───────┴──┘
      63 + ? = ?
      existing new total
      seats seats seats

      To make it a bit easier to write, let's pick some letters to represent those unknown numbers:
      - Let N = number of new seats to be added.
      - Let T = total number of seats after installation.

      Now we can think of it like this, using those letters:
      ┌───────┐ ┌──┐ ┌───────┬──┐
      Row 1: │•••••••│ + │••│ = │•••••••│••│
      Row 2: │•••••••│ + │••│ = │•••••••│••│
      Row 3: │•••••••│ + │••│ = │•••••••│••│
      Row 4: │•••••••│ + │••│ = │•••••••│••│
      Row 5: │•••••••│ + │••│ = │•••••••│••│
      Row 6: │•••••••│ + │••│ = │•••••••│••│
      Row 7: │•••••••│ + │••│ = │•••••••│••│
      Row 8: │•••••••│ + │••│ = │•••••••│••│
      Row 9: │•••••••│ + │••│ = │•••••••│••│
      └───────┘ └──┘ └───────┴──┘
      63 + N = T
      existing new total
      seats seats seats

      And now we can express that as a mathematical equation:

      63 + N = T

      T is the number we want to find (which is the total number of seats after the installation of new seats), but in order to do that, we first need to figure out the value of N, which is the number of new seats they will add. They didn't tell us what that number is, but they gave us some clues that we can use to figure it out. Earlier, they said there are 9 rows, and they will add 2 seats for each row, so we can figure out N like this:

      N = 9 × 2 = 18

      Now we know the value of N is 18, so let's fill that in.
      ┌───────┐ ┌──┐ ┌───────┬──┐
      Row 1: │•••••••│ + │••│ = │•••••••│••│
      Row 2: │•••••••│ + │••│ = │•••••••│••│
      Row 3: │•••••••│ + │••│ = │•••••••│••│
      Row 4: │•••••••│ + │••│ = │•••••••│••│
      Row 5: │•••••••│ + │••│ = │•••••••│••│
      Row 6: │•••••••│ + │••│ = │•••••••│••│
      Row 7: │•••••••│ + │••│ = │•••••••│••│
      Row 8: │•••••••│ + │••│ = │•••••••│••│
      Row 9: │•••••••│ + │••│ = │•••••••│••│
      └───────┘ └──┘ └───────┴──┘
      63 + 18 = T
      existing new total
      seats seats seats

      And we can put that into our mathematical equation too:
      63 + N = T
      63 + (9 × 2) = T
      63 + 18 = T

      Great! Now we have enough information to solve the original question! What we want is T – the total number of seats after the installation – so all we have left to do is add 63+18:
      63 + N = T
      63 + (9 × 2) = T
      63 + 18 = T
      81 = T

      So the value of T is 81 – this is the total number of seats there'll be after the new seats are added, which is what the question was asking!
      ┌───────┐ ┌──┐ ┌───────┬──┐
      Row 1: │•••••••│ + │••│ = │•••••••│••│
      Row 2: │•••••••│ + │••│ = │•••••••│••│
      Row 3: │•••••••│ + │••│ = │•••••••│••│
      Row 4: │•••••••│ + │••│ = │•••••••│••│
      Row 5: │•••••••│ + │••│ = │•••••••│••│
      Row 6: │•••••••│ + │••│ = │•••••••│••│
      Row 7: │•••••••│ + │••│ = │•••••••│••│
      Row 8: │•••••••│ + │••│ = │•••••••│••│
      Row 9: │•••••••│ + │••│ = │•••••••│••│
      └───────┘ └──┘ └───────┴──┘
      63 + 18 = 81
      existing new total
      seats seats seats
      (9 votes)
  • hopper happy style avatar for user karrbro000@student.sumnersd.org
    In he said rows and are'nt they collums?
    (3 votes)

Video transcript

A theater has a total of 63 seats in a rectangular grid. Here they are, right over here. It currently has 9 rows, each with an equal number of seats. We see that-- 1, 2, 3, 4, 5, 6, 7, 8, 9 rows. How many total seats will it have if it adds 2 seats per row? So what we want to figure out is the total number of seats. So let's say that the total is going to be equal to the number of seats that the theater already has. And they tell us that they have 63 seats in a rectangular grid. So it's going to be 63 seats plus the new seats, plus however many it adds. So plus the new seats. Well, what are the new seats going to be? Well, the new seats are going to be-- I have 9 rows, and I'm adding 2 seats per row. So the new seats are going to be 9 rows times 2 seats per row. So we could say that the total is going to be equal to 63 plus 9 times 2. And we 'll talk more about order of operations. But clearly, in this situation, we want to multiply 9 times 2 to figure out the total new number of seats. And then we want to add that to 63. And if we just write it like this, multiplication takes-- you will always do multiplication. And when you just see it in a row like this, you'll do the multiplication before you do the addition. So this is literally saying, hey, multiply 9 times 2 first, then add to 63, which is exactly what we care about. And what is 9 times 2? Well, let's add those 2 seats per row. So that's 2, 4, 6, 8, 10, 12, 14, 16, and 18. So 2 times 9. 2, 4, 6, 8, 10, 12, 14, 16, 18 is 18. So we're adding 18 new seats. So let me write this down. I covered up my old total. So total is equal to 63 plus 18. I had 63 seats. I'm now adding 18 seats. So total-- my total number of seats-- is now going to be 63 plus 18. Let's see, 8 plus 3 is 11. 60 plus 10 is 70. 70 plus 11 is going to be-- I have 80-- I have 81 seats. I now have 9 rows with 9 seats each, which gets me 81 total.