A cellulose solution contains 5% cellulose by weight in water. It is to be diluted to 4.0 % using a 1% solution of cellulose in water. Determine the kilograms of 1% solution required to dilute 100 kg of the 5% solution.
25%
To solve this problem, we need to find the amount of 1% solution required to dilute 100 kg of the 5% solution.
Step 1: Calculate the amount of cellulose in the original 5% solution.
The original 5% solution contains 5% cellulose by weight. Therefore, the amount of cellulose in 100 kg of the 5% solution is 5 kg (5% of 100 kg).
Step 2: Calculate the amount of cellulose in the final 4% solution.
The final 4% solution contains 4% cellulose by weight. Therefore, the amount of cellulose in the final solution should be 4% of the total weight after dilution.
Let's assume the total weight after dilution is x kg. Therefore, the amount of cellulose in the final solution is 0.04x kg.
Step 3: Calculate the amount of cellulose from the 1% solution.
The 1% solution contains 1% cellulose by weight. Therefore, the amount of cellulose in x kg of the 1% solution is 0.01x kg.
Step 4: Set up an equation to find x.
Since the amount of cellulose in the original 5% solution should be the same as the amount of cellulose in the final 4% solution, we can set up the following equation:
5 kg = 0.04x kg + 0.01x kg
Step 5: Solve the equation.
Combining like terms, we have:
5 kg = 0.05x kg
Dividing both sides of the equation by 0.05, we get:
x = 100 kg
Therefore, the total weight after dilution is 100 kg.
Step 6: Calculate the amount of 1% solution required to dilute the 100 kg of the 5% solution.
To calculate the amount of 1% solution required, we need to find the difference between the total weight after dilution and the weight of the original 5% solution.
The amount of 1% solution required is:
100 kg - 100 kg = 0 kg
Therefore, no 1% solution is required to dilute the 100 kg of the 5% solution, as the total weight after dilution is already 100 kg.
To solve this problem, we need to calculate the amount of cellulose in the 5% solution and determine the amount of the 1% solution needed to dilute it.
Let's start by calculating the amount of cellulose in the 5% solution.
Step 1: Calculate the weight of cellulose in the 5% solution.
In a 100 kg solution, the amount of cellulose is 5% of 100 kg.
Cellulose weight = 5/100 * 100 kg = 5 kg
Now, let's determine the amount of the 1% solution needed to dilute the 5% solution to 4%.
Step 2: Calculate the desired amount of cellulose in the diluted solution.
In a 100 kg solution, the amount of cellulose in the 4% solution is 4% of 100 kg.
Cellulose weight in the diluted solution = 4/100 * 100 kg = 4 kg
Step 3: Calculate the amount of cellulose in the 1% solution.
In a 100 kg solution, the amount of cellulose in a 1% solution is 1% of 100 kg.
Cellulose weight in the 1% solution = 1/100 * 100 kg = 1 kg
Step 4: Calculate the amount of 1% solution needed.
The difference in cellulose weight between the two solutions is 5 kg - 4 kg = 1 kg.
Since the 1% solution has 1 kg of cellulose, we need to use 1 kg of the 1% solution to dilute the 5% solution.
Therefore, we need 1 kg of the 1% solution to dilute 100 kg of the 5% solution.
Let x =kg of 1%.
(100 kg*5) = (x*1) = (100+x)*4
Solve for x.