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Lesson 3: One and two-step word problems

# 2-step word problem: theater

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

## Want to join the conversation?

• What if they removed 2 seats per row instead? • HOw do you do this!People are so smart here. • Is it too late to start this if I'm 13? • How do you get 81 for the answer • what is 360x500? • Could we use multiplication. • Do you now 1000 times 1000 • thank you for this video it help me a lot • hey SebastianF • how would u explain the probalom easiar for someone who is just starting this
(1 vote) • 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`