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### Course: 3rd grade (Eureka Math/EngageNY) > Unit 1

Lesson 6: Topic F: Distributive property and problem solving using units of 2–5 and 10- Properties of multiplication
- Visualize distributive property
- Distributive property when multiplying
- Distributive property
- 2-step word problem: theater
- 2-step word problem: truffles
- 2-step word problem: running
- 2-step estimation problem: marbles
- 2-step word problems

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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.

## Want to join the conversation?

- What if they removed 2 seats per row instead?(30 votes)
- then u would do 63-9*2 because it comes from the 63(9 votes)

- isn't nine times nine 81?(13 votes)
- Yes 9×9=81. Good Job! Keep studying and you'll learn more multication and the other 3 tables. And other math! You know what they say,"Practice makes perfect".(11 votes)

- How would you explain the problem easily for someone who is just starting this?(4 votes)
- 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`

(24 votes)

- In2:24he said rows and are'nt they collums?(9 votes)
- No, rows go horizontally and columns go vertically. In the video there are 9 rows and 7 columns (not counting the green blocks). Think of an actual column in real life and how it goes straight up(12 votes)

- this is a waste of time(8 votes)

- what if we removed 2 seats per row instead?(3 votes)
- then you would do 63-18(4 votes)

- 21/7x2 is what number.(4 votes)
- Well. Firstly, we do
`21/7`

below:`21`

—— = 3

7

Now, with this answer we have to now multiply it by`2`

.`3`

x 2

———

6

The answer is`6`

. In conclusion, the answer of`21 / 7 x 3`

is

.**6***Hope this helps!*(1 vote)

- this is arrays am i right !(2 votes)
- Yes! This question does include arrays.
*Hope this helps!*(1 vote)

## 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.