Question

Blue and green dye or mixed in a 7 to 4 ratio to make 44 L of tea. Cut a die before that 8 L of green dye or added to the mixture. What is the new ratio of blue to green dye in simplest form?

Answer 1

To find the new ratio of blue to green dye, first calculate the amounts of blue and green dye in the original mixture. Then, add the additional green dye and calculate the new ratio. The new ratio of blue to green dye in simplest form is 7:6.

Step-by-step explanation:

To find the new ratio of blue to green dye, we first need to determine the amounts of blue and green dye in the original mixture.

Initially, the blue and green dye were mixed in a 7 to 4 ratio. This means that for every 7 units of blue dye, there were 4 units of green dye.

Given that a total of 44 L of tea was made, we can calculate the amounts of blue and green dye in the original mixture as follows:

Blue dye: 7/11 × 44 L = 28 L

Green dye: 4/11 × 44 L = 16 L

Next, 8 L of green dye is added to the mixture. This means the new amount of green dye is 16 L + 8 L = 24 L.

The new ratio of blue to green dye can be calculated as:

Blue to green dye ratio = 28 L : 24 L = 7: 6

Therefore, the new ratio of blue to green dye in simplest form is 7:6.

Answer 2

To find the new ratio of blue to green dye after adding 8 L of green dye to the mixture, we need to calculate the new amounts of blue and green dye.

Let's first determine the initial amounts of blue and green dye in the mixture. The ratio of blue to green dye is given as 7 to 4. This means that for every 7 parts of blue dye, there are 4 parts of green dye.

Since we have a total of 44 L of tea, we can divide it into 11 parts (7 + 4) to determine the size of each part. Each part would be equal to 44 L divided by 11, which is 4 L.

Next, let's calculate the initial amounts of blue and green dye. Multiplying 4 L by 7, we get 28 L of blue dye, and multiplying 4 L by 4, we get 16 L of green dye in the original mixture.

Now, we can calculate the new amounts of blue and green dye after adding 8 L of green dye. Adding 8 L to the initial 16 L of green dye, we get a total of 24 L of green dye in the mixture.

Since the ratio of blue to green dye is now 28 L to 24 L, we can simplify it by dividing both amounts by their greatest common divisor, which is 4. Simplifying 28 L divided by 4, we get 7 L of blue dye. Simplifying 24 L divided by 4, we get 6 L of green dye.

Therefore, the new ratio of blue to green dye in the simplest form is 7 to 6.

In summary:

- Initial ratio of blue to green dye: 7 to 4

- Initial amounts of blue and green dye: 28 L and 16 L, respectively

- After adding 8 L of green dye, the new amounts of blue and green dye: 7 L and 6 L, respectively

- New ratio of blue to green dye: 7 to 6

Step-by-step explanation:

Hope This HELPS