1/3 of the 6 dozen fruits in a fruit seller's cart are apples.If 1/4 of all the fruits are oranges and the rest of the fruits are bananas,find how many dozen of bananas are there in a fruit seller's cart?

1/3 of 6 dozen fruits are apples = 2 dozen apples.

1/4 of 6 dozen fruits are oranges = 1 1/2 dozen are oranges.

2 dozen apples

1 1/2 dozen oranges

6 - 3 1/2 = 2 1/2 dozen bananas

2.5

2 APPLES

1 1/2 ORANGES

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1 / 3 of 6 dozen fruits are apples means:

1 / 3 ∙ 6 = 6 / 3 = 2 dozen apples

1 / 4 of all the fruits are oranges means:

1 / 4 ∙ 6 = 6 / 4 = 2 ∙ 3 / 2 ∙ 2 = 3 / 2 = 1.5 dozen oranges

The rest of the fruits are bananas means:

6 dozen fruits - 2 dozen apples - 1.5 dozen oranges are bananas.

6 - 2 - 1.5 = 2.5 dozen bananas

To solve this problem, we need to find out how many fruits are in a cart and then determine the number of bananas. Here's how we can do it step by step:

Step 1: Find the total number of fruits in the cart.
Since there are 6 dozen fruits, which is equal to 6 x 12 = 72, the cart contains 72 fruits.

Step 2: Calculate the number of apples.
One-third of the fruits in the cart are apples. So, we can find the number of apples by multiplying the total number of fruits (72) by 1/3:
Number of apples = 72 x 1/3 = 24

Step 3: Calculate the number of oranges.
One-fourth of the fruits are oranges. Therefore, we can calculate the number of oranges by multiplying the total number of fruits (72) by 1/4:
Number of oranges = 72 x 1/4 = 18

Step 4: Calculate the number of bananas.
Now, we need to find the number of bananas. Since the apples and oranges accounted for 24 + 18 = 42 fruits, the remaining fruits in the cart must be bananas.
Number of bananas = Total number of fruits - (Number of apples + Number of oranges)
Number of bananas = 72 - 42 = 30

Step 5: Convert the number of bananas into dozens.
We were given the number of fruits in dozens, so we need to convert the number of bananas into dozens. Since there are 12 fruits in one dozen, we divide the number of bananas by 12 to obtain the number of dozen bananas:
Number of dozen bananas = Number of bananas / 12 = 30 / 12 = 2.5

Therefore, there are 2.5 dozen bananas in the fruit seller's cart.