How many liters of a 2.5% bleach solution must be mixed with a 10% bleach solution to produce 600 ml of a 5% bleach solution?
amount of weaker solution --- x L
amount of stronger solution -- (600-x)
solve for x
.025x + .1(600-x) = .05(600)
To determine the amount of each bleach solution needed, we can set up an equation based on the amount of pure bleach in each solution.
Let's denote:
x = volume (in liters) of the 2.5% bleach solution
y = volume (in liters) of the 10% bleach solution
We know that the resulting volume needed is 600 ml, which is equivalent to 0.6 liters.
Now let's write the equation based on the amount of pure bleach in each solution:
0.025x + 0.10y = 0.05 * 0.6
Simplifying the equation:
0.025x + 0.10y = 0.03
Since we need to find the amount of each solution, we have two unknowns, but we can use the fact that the total volume must equal 0.6 liters:
x + y = 0.6
Now we have a system of equations:
0.025x + 0.10y = 0.03
x + y = 0.6
To solve this system, we can use substitution or elimination methods. Let's use the substitution method:
Rearrange the second equation:
x = 0.6 - y
Substitute this value of x in the first equation:
0.025(0.6 - y) + 0.10y = 0.03
Multiply and distribute:
0.015 - 0.025y + 0.10y = 0.03
Combine like terms:
0.075y = 0.015
Divide by 0.075:
y = 0.2
Now substitute this value of y into the second equation to find x:
x + 0.2 = 0.6
x = 0.6 - 0.2
x = 0.4
Therefore, to produce 600 ml of a 5% bleach solution, you need 0.4 liters of a 2.5% bleach solution and 0.2 liters of a 10% bleach solution.
To solve this problem, we need to use the concept of concentration and mixtures. Here's how we can calculate the number of liters of each bleach solution needed:
Let's denote:
x = the volume (in liters) of the 2.5% bleach solution
y = the volume (in liters) of the 10% bleach solution
First, let's convert the volume of the final solution to liters:
600 ml = 600/1000 = 0.6 liters
Next, let's write down the equation for the concentration of bleach in the final solution:
0.05 (5% bleach concentration) = (Volume of bleach in 2.5% solution + Volume of bleach in 10% solution) / (Total volume of the mixture)
Now, let's substitute the values we have into the equation:
0.05 = (0.025x + 0.10y) / (x + y)
Since we are looking for the specific volume of the 2.5% bleach solution, we can isolate x in the equation.
Multiply both sides of the equation by (x + y) to eliminate the denominator:
0.05(x + y) = 0.025x + 0.10y
Distribute the multiplication on the left side:
0.05x + 0.05y = 0.025x + 0.10y
Move the variables to one side and the constants to the other side:
0.05x - 0.025x = 0.10y - 0.05y
0.025x = 0.05y
Divide both sides of the equation by 0.025:
x = 2y
Now, we have an equation relating the volume of the 2.5% bleach solution to the volume of the 10% bleach solution.
Next, let's consider the total volume of the mixture. Since we want a total of 0.6 liters, we can write another equation:
x + y = 0.6
Now, we can substitute the value of x from the previous equation into this equation:
2y + y = 0.6
3y = 0.6
y = 0.2
Substituting this y value back into the equation x = 2y, we get:
x = 2(0.2)
x = 0.4
Therefore, you would need 0.4 liters of the 2.5% bleach solution and 0.2 liters of the 10% bleach solution to produce 600 ml of a 5% bleach solution.