2/3 of the baked goods in a bakery are pastries. 5/6 of the pastries are sweet. Gerry packs 1/5 of the sweet pastries equally into 3 boxes. What fraction of all the baked goods are in each box?
2 / 3 ∙ 5 / 6 = 2 ∙ 5 / 3 ∙ 6 = 10 / 18 = 2 ∙ 5 / 2 ∙ 9 = 5 / 9 of the pastries are sweet
1 / 5 of the sweet pastries = 1 / 5 ∙ 5 / 9 = 1 ∙ 5 / 5 ∙ 9 = 1 / 9
( 1 / 9 ) / 3 = 1 / 9 ∙ 3 = 1 / 27 of all the baked goods are in each box
To find the fraction of all the baked goods that are in each box, we need to calculate the fraction of the sweet pastries that Gerry packs into each box and then multiply it by the fraction of pastries out of all the baked goods.
Given information:
- 2/3 of the baked goods are pastries.
- 5/6 of the pastries are sweet.
- Gerry packs 1/5 of the sweet pastries equally into 3 boxes.
First, let's calculate the fraction of sweet pastries that Gerry packs into each box. To do this, we multiply 1/5 by 5/6:
(1/5) * (5/6) = 1/6
So, 1/6 of the sweet pastries are packed into each box.
Next, let's calculate the fraction of all the baked goods that are pastries. We know that 2/3 of the baked goods are pastries, so 2/3 is the fraction of all the baked goods that are pastries.
Finally, to find the fraction of all the baked goods that are in each box, we multiply the fraction of sweet pastries in each box by the fraction of all the baked goods that are pastries:
(1/6) * (2/3) = 2/18 = 1/9
Therefore, each box contains 1/9 of all the baked goods.
To find the fraction of baked goods in each box, we need to calculate the fraction of all the baked goods that were packed into the boxes.
Let's break down the problem step by step:
1. Start with the total number of baked goods.
Since 2/3 of the baked goods are pastries, that means the remaining 1/3 are not pastries. Let's assume the total number of baked goods is represented by the variable "b".
2. Calculate the number of pastries.
Since 2/3 of the baked goods are pastries, we can find the number of pastries using the equation: (2/3) * b = number of pastries.
3. Calculate the number of sweet pastries.
Since 5/6 of the pastries are sweet, we can find the number of sweet pastries using the equation: (5/6) * (2/3) * b = number of sweet pastries.
4. Calculate the number of sweet pastries packed into the boxes.
Gerry packs 1/5 of the sweet pastries equally into 3 boxes. Thus, the number of sweet pastries in each box is: (1/5) * (5/6) * (2/3) * b / 3 = number of sweet pastries in each box.
5. Simplify the fraction.
To simplify the fraction, you can multiply the numerator and the denominator by the same number to get an equivalent fraction.
By following this process, you can calculate the fraction of all the baked goods that are in each box.