John mixed 3\4 liters of yellow paint with 1 1\4 liters of red paint to make 2 liters of orange paint.
He needed more orange paint.
to make a new batch of orange paint, he used exactly 1 liter of red paint
using the same ratio, how many liters of yellow paint should john use to make the new batch of orange paint
yellow:red = 3:5
if red=1, divide by 5 to get 3/5 : 5/5 = 3/5 : 1
so, yellow = 3/5
To find out how many liters of yellow paint John should use to make the new batch of orange paint, we need to determine the ratio of yellow paint to red paint from the original mixture.
In the original mixture, John mixed 3/4 liters of yellow paint with 1 1/4 liters of red paint to make 2 liters of orange paint.
To determine the ratio of yellow paint to red paint, we can set up a proportion:
Yellow paint / Red paint = Original orange paint / Required orange paint
Let's plug in the numbers from the original mixture:
(3/4) / (1 1/4) = 2 / Required orange paint
Now, let's solve for the required orange paint:
(3/4) / (5/4) = 2 / Required orange paint
To simplify the left side of the equation, we can multiply the numerator and denominator of the fraction by 4:
(3/4) * (4/5) = 2 / Required orange paint
Now, we can simplify further:
(3/5) = 2 / Required orange paint
To isolate the variable on one side, we can cross multiply:
(3/5) * Required orange paint = 2
Now, let's solve for the required orange paint:
Required orange paint = (2 * 5) / 3
Required orange paint = 10/3
So, John needs to use 10/3 liters of yellow paint to make the new batch of orange paint.
To find out how many liters of yellow paint John should use to make the new batch of orange paint, we can use the ratio from the first batch.
In the first batch, John mixed 3/4 liters of yellow paint with 1 1/4 liters of red paint to make 2 liters of orange paint.
The ratio of yellow paint to red paint in the first batch is 3/4 : 1 1/4.
To use this ratio to find the amount of yellow paint needed for the new batch, we set up a proportion.
Let x be the number of liters of yellow paint needed for the new batch.
The ratio of yellow paint to red paint in the new batch is x : 1.
So we have the proportion:
(3/4) / (1 1/4) = x / 1
To simplify the proportion, we convert 1 1/4 to an improper fraction:
1 1/4 = 5/4
Now, we can rewrite the proportion as:
(3/4) / (5/4) = x / 1
To solve the proportion, we can cross-multiply:
(3/4) * 4 = x * 5
3 = 5x
Now, we can solve for x by dividing both sides of the equation by 5:
3/5 = x
Therefore, John should use 3/5 liters of yellow paint to make the new batch of orange paint.