Final answer:
Yara can put 3 cookies of a single type in each basket as the Greatest Common Divisor (GCD) of 12, 9, and 15 is 3.
Step-by-step explanation:
To find the greatest number of cookies Yara can put in each basket without mixing them, we need to find the greatest divisor that is common to all three numbers of cookies. This is called the Greatest Common Divisor (GCD).
First we list the factors of each:
- 12: 1, 2, 3, 4, 6, 12
- 9: 1, 3, 9
- 15: 1, 3, 5, 15
The common divisors for all three numbers are 1 and 3. The greatest of these is 3.
Therefore, Yara can place 3 cookies in each basket, of one type of cookie. This implies that she will have several baskets, each containing 3 cookies of the same type and no other variety.