Final answer:
Nina is correct in believing that the greatest number of fruit baskets they can make is 9. The error made by Maylin is incorrectly finding the greatest common divisor. Each basket will have 4 apples, 3 bananas, and 2 oranges.
Step-by-step explanation:
To determine who is correct between Maylin and Nina about the greatest number of fruit baskets they can make, we need to find the greatest common divisor (GCD) of the quantity of apples (36), bananas (27), and oranges (18). In this case, the GCD is 9, meaning that Nina is correct, and they can make 9 baskets with an equal number of each fruit.
Maylin's error was that she did not find the GCD correctly. The GCD is the largest number that divides into each of the given numbers without leaving a remainder. In this instance, 6 is not the GCD because it is not the largest number that can divide into all three fruit counts without a remainder.
To find the number of each fruit in each basket, we divide the total count of each fruit by the number of baskets:
- Apples in each basket: 36 apples ÷ 9 baskets = 4 apples
- Bananas in each basket: 27 bananas ÷ 9 baskets = 3 bananas
- Oranges in each basket: 18 oranges ÷ 9 baskets = 2 oranges