Dilbert needs to mix a 10% alcohol solution with a 30% alcohol solution to create 100 millileters of a 16% solution. How many millileters of each solution must Dilbert use?
a+b=100
.1a = 3B=.16(100)
To solve this problem, let's use a system of equations.
Let x represent the volume (in milliliters) of the 10% alcohol solution that Dilbert needs to use.
Let y represent the volume (in milliliters) of the 30% alcohol solution that Dilbert needs to use.
We know that the total volume of the final solution should be 100 milliliters, so the first equation is:
x + y = 100 -- Equation 1
Next, let's consider the amount of alcohol in each solution. The 10% alcohol solution has 10% of alcohol per milliliter, and Dilbert is using x milliliters of it, so the amount of alcohol from this solution is 0.1x. Similarly, the amount of alcohol from the 30% alcohol solution is 0.3y.
Since Dilbert wants to create a 16% alcohol solution, the total amount of alcohol in the final solution is 16% of 100 milliliters, which is 0.16(100) = 16 milliliters. Therefore, the second equation is:
0.1x + 0.3y = 16 -- Equation 2
Now we have a system of equations:
x + y = 100 -- Equation 1
0.1x + 0.3y = 16 -- Equation 2
To solve this system, we can use the method of substitution or elimination. Let's use the substitution method.
Solve Equation 1 for x:
x = 100 - y
Substitute this expression for x into Equation 2:
0.1(100 - y) + 0.3y = 16
Simplify and solve for y:
10 - 0.1y + 0.3y = 16
0.2y = 6
y = 30
Now substitute the value of y = 30 back into Equation 1 to find x:
x + 30 = 100
x = 70
Therefore, Dilbert needs to use 70 milliliters of the 10% alcohol solution and 30 milliliters of the 30% alcohol solution to create 100 milliliters of a 16% solution.
To solve this problem, we can use a basic algebraic approach. Let's assume Dilbert uses x milliliters of the 10% alcohol solution and (100 - x) milliliters of the 30% alcohol solution.
Since he wants a 100 milliliter solution with a 16% alcohol concentration, we can set up the equation:
(0.10x + 0.30(100 - x)) / 100 = 0.16
Let's break it down:
- The first part, 0.10x, represents the amount of alcohol in x milliliters of the 10% alcohol solution. Since the concentration is given as a percentage, we convert it to a decimal by dividing by 100.
- The second part, 0.30(100 - x), represents the amount of alcohol in (100 - x) milliliters of the 30% alcohol solution.
- Then we divide the sum of these two amounts by 100, which is the total volume of the solution, to get the average alcohol concentration of 0.16 (16%).
Now, we can solve the equation for x to find the value of x (the number of milliliters of the 10% solution).
0.10x + 0.30(100 - x) = 0.16 * 100
0.10x + 30 - 0.30x = 16
30 - 16 = 0.30x - 0.10x
14 = 0.20x
x = 14 / 0.20
x = 70
Therefore, Dilbert needs to use 70 milliliters of the 10% alcohol solution and (100 - 70) = 30 milliliters of the 30% alcohol solution in order to create a 100 milliliter solution with a 16% alcohol concentration.