Give a button and a bookmark

to each student who visited the fair. The buttons came in

packages of 30. The bookmarks came in packages of 50.

The committee needed the same number of each left

over for another fair. The committee estimated that

400 students would visit the fair. How many

packages of buttons and packages of bookmarks

did they need?

15 packages of buttons

9 packages of bookmarks

Step-by-step explanation:

We need to find the least common multiple (LCM) of 30 and 50.

30 = 2*3*5

50 = 2*5²

LCM = 2*3*5²

LCM = 150

Now we need to find a multiple of LCM that is greater than 400.

3LCM = 450

The committee needs at least 450 of each, which means they need at least 15 packages of buttons and 9 packages of bookmarks.

Let's note the information.

This is what we know:

Every buttons came in packages of 30 per student.

Every bookmark came in packages of 50 per person.

Know, we need to do some multiplying.

30 x 400 & 50 x 400

Now solve.

30 X 400 = 12000.

So we now know that they have an estimated 12000 buttons total.

Now, we find x for bookmarks.

50 x 400 = 20000

That means total that estimated that 20000 bookmarks will be given.