yellow:red = 3:5
if red=1, divide by 5 to get 3/5 : 5/5 = 3/5 : 1
so, yellow = 3/5
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
if red=1, divide by 5 to get 3/5 : 5/5 = 3/5 : 1
so, yellow = 3/5
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.
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.