Question

Shelby wants to advertise her duct tape business, so she gives sets of 15 red flyers to each teacher in grades K-2 and sets of 20 blue flyers to each teacher in grades 3-5. At the end of the day, Shelby realizes that she gave out the same number of red and blue flyers. What is the minimum number of each color she distributed?

Answer 1

The minimum number of red and blue flyers Shelby distributed is 60 each, which is the least common multiple (LCM) of 15 and 20. Therefore, there must be at least 4 teachers in grades K-2 and at least 3 teachers in grades 3-5 for the flyers to be distributed evenly.

Step-by-step explanation:

To find the minimum number of red and blue flyers that Shelby distributed, we need to find the least common multiple (LCM) of the two sets she gave out, 15 red flyers for grades K-2 and 20 blue flyers for grades 3-5.

Let's find the LCM of 15 and 20, which will give us the smallest number that both 15 and 20 divide into evenly:

1. Prime factors of 15: 3 x 5
2. Prime factors of 20: 22 x 5

LCM = 22 x 3 x 5 = 4 x 3 x 5 = 60

Therefore, the minimum numbers of red and blue flyers Shelby distributed are both 60.

Since Shelby gave sets of 15 red flyers, there were at least 4 teachers in grades K-2 and since she gave sets of 20 blue flyers, there were at least 3 teachers in grades 3-5 for the numbers of flyers to be equal.