John's birthday is this saturday, in buying materials for the party Vicki notices that plates come in packs of 12, cups come in packs of 10, and utensils come in packs of 8 sets. If Vicki wants to have no left overs, how many packs of utensils should she buy?

Step-by-step explanation:

So, Vicki wants no left overs whatsoever, which means we have to get all three items to the same number. We first look at 10. We know that 10 will always have a 0 in the one's place, meaning that 8 and 12 have to be multiplied by 5, 10, 15, 20, etc., but they do not need to be multiplied by the same number.

Let's take 8 first. 8 can possibly go up to 40, 80, 120, 160, 200, etc.

Then 12. 12 can possibly go up to 60, 120, 180, 220, 280, etc.

We can see that both numbers have 120 in common, so we shall use that.

We know that we can get 10 to 120 by multiplying 10 by 12, meaning Vicki buys 12 packs of cups.

We know that we can get 12 to 120 by multiplying 12 by 10, meaning Vicki buys 10 packs of plates.

And finally, we know that we can get 8 to 120 by multiplying 8 by 15, meaning Vicki buys 15 packs of utensils.

So, since the question is asking for utensils only, we should say that Vicki buys 15 packs of utensils.

irrational, cannot