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CCSS.Math:

Akshay brought four boxes of
chocolate truffles to a party. Each box contains 6 truffles. Every guest at the party
ate exactly 3 truffles, and there were none left over. How many guests
must there have been at the party, must have
attended the party? So we're trying to figure
out how many guests must have attended the party. So let's actually define a
letter to represent that. So let's say that p, or
let's say g, g for guests, let's say that g is equal to the
number of guests at the party. Then we could actually
set up a relation between the number of guests,
the number of truffles each guest ate, and then the
total number of chocolates. So what was the total
number of chocolates that we have at this party? Well, he bought 4 boxes. And each box
contains 6 truffles. So the total number of
chocolates at the party must have been 4 times 6. 4 times 6 truffles
must have been the total number of
truffles at the party. So let me write this down. This is the number
of truffles total. Now, what's another
way of thinking about the total number
of truffles at the party? Well, you have g guests. So you have g guests. And each guest ate 3 truffles. So g times 3 is also going
to be the number of truffles at the party-- number
of truffles total. So these two things need
to be equal to each other. So we could figure
out what 4 times 6 is. And then we say, well, 4 times
6 is going to be some number. And g times 3 has to
equal that same number. What must g be? So let's think about
that step by step. So let's just
visualize 4 times 6. So here is one box of truffles. We get 6 truffles. So it's 1 times 6, 2 times
6, 3 times 6, and 4 times 6. Or another way of
thinking about 4 times 6, that's the same thing
as 6 plus 6 plus 6 plus 6, which is 6, 12, 18, 24. So what we have here on
the left hand side is 24. So we get 24. And now we know
that this is going to be equal to the number
of guests at the party. This is going to be equal to the
number of guests at the party times 3. So what times 3 is equal to 24? And another way of viewing this
is if g times 3 is equal to 24, that means that 24 divided
by 3 must be equal to g. So one way of thinking
about it, if I were to divide these
truffles, these 24 truffles, into groups of 3,
3 for each guest, well, the number of
groups I'm going to have will tell me the number
of guests I have. So let's do that. So let's divide it
into groups of 3. So let's see. Here is one group of
3, right over here. One group of 3. And now I have another group
of 3, so two groups of 3. And now I have
three groups of 3. Here's four groups of 3. Here is five groups of 3, six
groups of 3, seven groups of 3, and eight groups of 3. So if I were to take 24 things
and divide it into groups of 3, I get 8 groups. So we see that g-- let
me get my pen tool. We see that g, or I
could say 24 divided by 3 is 8, which must be equal to the
number of guests at the party. The other way of thinking
about it is I'm like, hey, some mystery
number here, g, that I'm trying to
figure out, the number of guests at the party
times 3 is equal to 24. So what times 3 is 24? Well, you could just think about
all the multiples of three. 3 times 1 is 3. 3 times 2 is 6. 3 times 3 is 9,
12, 15, 18, 21, 24. That's three times 1,
2, 3, 4, 5, 6, 7, 8. 3 times 8 is 24, so
g must be equal to 8, or 8 must be equal to g. Or we had exactly 8
guests at our party.