Question

Taylor wishes to advertise her business, so she gives packs of 13 red flyers to each restaurant owner and sets of 20 blue flyers to each clothing store owner. At the end of the day, Taylor realizes that she gave out the same number of red and blue flyers. What is the minimum number of flyers of each color she distributed?​

Answer 1

Answer:

Let's call the number of packs of red flyers Taylor gave out "r" and the number of packs of blue flyers she gave out "b". We know that each pack contains 13 red flyers and 20 blue flyers. So the total number of red flyers is 13r and the total number of blue flyers is 20b.

We also know that Taylor gave out the same number of red and blue flyers. In other words:

13r = 20b

To find the minimum number of flyers of each color, we want to find the smallest integer values of r and b that satisfy this equation. One way to do this is to find the least common multiple (LCM) of 13 and 20, and then divide by 13 and 20 to get r and b, respectively.

The prime factorization of 13 is 13, and the prime factorization of 20 is 2 x 2 x 5. The LCM of 13 and 20 is 2 x 2 x 5 x 13 = 520.

So:

13r = 20b

13r = (13/4) x (80b)

r = (13/4) x (80b) / 13

r = 20b

We can see that r = 20b is the smallest integer value that satisfies the equation. Therefore, Taylor distributed a minimum of:

13r = 13 x 20b = 260 red flyers

20b = 20 x 20b = 400 blue flyers

So Taylor distributed a minimum of 260 red flyers and 400 blue flyers.

Explanation:

Answer 2

Let's call the number of packs of red flyers Taylor gave out "r" and the number of packs of blue flyers she gave out "b". We know that each pack contains 13 red flyers and 20 blue flyers. So the total number of red flyers is 13r and the total number of blue flyers is 20b.

We also know that Taylor gave out the same number of red and blue flyers. In other words:

13r = 20b

To find the minimum number of flyers of each color, we want to find the smallest integer values of r and b that satisfy this equation. One way to do this is to find the least common multiple (LCM) of 13 and 20, and then divide by 13 and 20 to get r and b, respectively.

The prime factorization of 13 is 13, and the prime factorization of 20 is 2 x 2 x 5. The LCM of 13 and 20 is 2 x 2 x 5 x 13 = 520.

So:

13r = 20b

13r = (13/4) x (80b)

r = (13/4) x (80b) / 13

r = 20b

We can see that r = 20b is the smallest integer value that satisfies the equation. Therefore, Taylor distributed a minimum of:

13r = 13 x 20b = 260 red flyers

20b = 20 x 20b = 400 blue flyers

So Taylor distributed a minimum of 260 red flyers and 400 blue flyers.