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Video transcript

akshay brought four boxes of chocolate truffles to a party each box contains six truffles every guest at the party ate exactly three truffles and there were none left over how many guests must there been at the party must have attended the party so we're trying to figure out how many guests how many guests must have attended the party so let's actually 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 the 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 guests ate and then the total number of chocolates so what was a total number of chocolates that we have at this party well he bought four boxes and each box contains six truffles so the total number of chocolates at the party must have been four times six four times six 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 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 guests ate three truffles each guests ate three truffles so G times three is also going to be the number of truffles at the party number of truffles total number of truffles total so these two things need to be equal to each other so we could figure out what four times six is and then we say well four times six is going to be some number and G times three has to equal that same number what must G be so let's think about that step by step so let's just visualize four times six so here is one box of truffles we get six truffles so it's one times six two times six three times six and four times six or another way of thinking about four times six 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 times 3 so what times 3 is equal to 24 in another way of viewing this another way of viewing this is if G times 3 is equal to 24 that means that 24 24 divided by 3 divided by 3 must be equal to G 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 guess 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 now I have 3 groups of 3 3 groups of 3 here's 4 groups of 3 here is 5 groups of 3 6 groups of 3 7 groups of 3 and 8 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 we see that G let me get my pin 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 three is 24 well you could just think about all the multiples of 3 3 times 1 is 3 3 times 2 is 6 3 times 3 is 9 12 15 18 21 24 that's 3 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