To make an orange dye, 4 parts of red dye are mixed with 3 parts of yellow dye. To make a green dye, 2 parts of blue dye are mixed with 1 part of yellow dye. If equal amounts of green dye and orange dye are mixed,___________ of this mixture is composed of yellow dye.
4/10
To find out the proportion of yellow dye in the mixture, we need to determine the ratio of orange dye to green dye.
Given:
Orange dye = 4 parts red dye + 3 parts yellow dye
Green dye = 2 parts blue dye + 1 part yellow dye
Let's assume we have the same amount of orange and green dye.
For orange dye, it consists of 3 parts yellow dye.
For green dye, it consists of 1 part yellow dye.
So, when equal amounts of orange and green dye are mixed, the resulting mixture will be composed of:
3 parts yellow dye (from orange dye) + 1 part yellow dye (from green dye) = 4 parts yellow dye.
Therefore, 4 parts of the mixture will be composed of yellow dye.
To find the proportion of yellow dye in the mixture, we need to calculate the ratio of yellow dye in both green and orange dyes separately.
For the orange dye:
- The ratio of red to yellow dye is 4:3.
- This means for every 7 parts of orange dye, there are 3 parts of yellow dye.
For the green dye:
- The ratio of blue to yellow dye is 2:1.
- This means for every 3 parts of green dye, there is 1 part of yellow dye.
When equal amounts of green and orange dyes are mixed, let's assume we have a total of 7 units of each dye.
In the orange dye:
- There are 3 units of yellow dye for every 7 units of orange dye.
In the green dye:
- There is 1 unit of yellow dye for every 3 units of green dye.
When equal amounts are mixed, the total amount of yellow dye is the sum of the yellow dye in each:
Yellow dye in the orange dye: (3/7) * 7 = 3 units
Yellow dye in the green dye: (1/3) * 7 = 2.33 units (rounded to 2 decimal places)
Therefore, when equal amounts of green and orange dyes are mixed, approximately 5.33 units (3 + 2.33) of the mixture will be composed of yellow dye.