Question

Callie is starting a fruit basket business. The largest fruit basket will contain 30 pieces of fruit. Other baskets may contain fewer, but at least 12 piece of fruit. In every basket, 1/2 of the pieces of fruit must be apples, 1/3 must be oranges, and 1/6 must be bananas. What combinations of pieces of fruit represent all the possible fruit baskets Callie can make?

Answer 1

In the first basket, Callie can make 15 apples, 10 oranges and 5 bananas.

In the second basket, she can make 12 apples, 8 oranges and 4 bananas and

in the third basket, she can make 9 apples, 6 oranges and 3 bananas.

Explanation:

The largest basket contains 30 pieces of fruit. So, it contains

1/2 of 30 = 15 apples

1/3 of 30 = 10 oranges and

1/6 of 30 = 5 bananas.

The second and third baskets should contain at least 12 pieces and at most 30 pieces (since the largest basket contains 30 pieces). Also, the number should be divided by 2, 3 and 6. So, it must be a multiple of 6.

Clearly, the number of multiples of 6 between 12 and 30 are 18 and 24.

Hence, the second basket contains 24 pieces of fruits and it contains

1/2 of 24 = 12 apples

1/3 of 24 = 8 oranges and

1/6 of 24 = 4 bananas

The third basket contains 18 pieces of fruits and it contains

1/2 of 18 = 9 apples

1/3 of 18 = 6 oranges and

1/6 of 18 = 3 bananas.