A nurse has two solutions that contain different concentrations of a certain medication. One is a 20% concentration and the other is a 5% concentration. How many cubic centimeters of each should he mix to obtain 10 cc of a 18.5% solution?

.20 x + [.05 (10 - x)] = .185 * 10

multiply by 100 ... 20 x + 50 - 5x = 185

To determine how many cubic centimeters (cc) of each solution the nurse should mix, we can set up a simple equation using the concept of concentrations:

Let's assume the nurse needs to mix x cc of the 20% concentration solution and (10 - x) cc of the 5% concentration solution to obtain a final 10 cc of 18.5% solution.

To find the concentration of the final solution, we can use the formula:

(total amount of medication in solution) / (total volume of solution)

For the 20% concentration solution, the total amount of medication is 0.20x (20/100 = 0.20) and the total volume is x cc.
For the 5% concentration solution, the total amount of medication is 0.05(10 - x) (5/100 = 0.05) and the total volume is (10 - x) cc.
For the final solution, the total amount of medication is 0.185(10) (18.5/100 = 0.185) and the total volume is 10 cc.

Setting up the equation:

0.20x + 0.05(10 - x) = 0.185(10)

Now, we can solve the equation to find the value of x:

0.20x + 0.5 - 0.05x = 1.85

0.20x - 0.05x = 1.85 - 0.5

0.15x = 1.35

x = 1.35 / 0.15

x = 9

Therefore, the nurse should mix 9 cc of the 20% concentration solution and (10 - 9) = 1 cc of the 5% concentration solution to obtain 10 cc of an 18.5% solution.

To solve this problem, we can use the method of alligation or the weighted average method. The goal is to find the ratio of the two solutions that need to be mixed.

Let's label the unknown quantity of the 20% concentration solution as "x" (in cc) and the unknown quantity of the 5% concentration solution as "y" (in cc). We want to find values for x and y such that, when they are mixed together, they will result in 10 cc of an 18.5% solution.

To calculate the ratio, we can set up a proportion based on the amount of the medication in each solution.

The amount of the medication in the 20% solution is 20% of x cc, which is 0.20x cc.
The amount of the medication in the 5% solution is 5% of y cc, which is 0.05y cc.

The total amount of the medication in the 10 cc mixture is 18.5% of 10 cc, which is 0.185 * 10 cc, or 1.85 cc.

Now we can set up the proportion:

0.20x / 10 + 0.05y / 10 = 1.85 / 10

Simplifying the equation gives us:

0.02x + 0.005y = 0.185

To solve for x and y, we need another equation. We can use the fact that the total volume of the mixture is 10 cc:

x + y = 10

Now we have a system of equations:

0.02x + 0.005y = 0.185
x + y = 10

We can solve this system using various methods, such as substitution or elimination. Here, we'll use the substitution method.

Rearrange the second equation to solve for x:

x = 10 - y

Substitute this expression for x into the first equation:

0.02(10 - y) + 0.005y = 0.185

Now simplify and solve for y:

0.2 - 0.02y + 0.005y = 0.185
0.195y = 0.015
y = 0.078

Now substitute the value of y back into the second equation to solve for x:

x + 0.078 = 10
x = 9.922

So, the nurse should mix approximately 9.922 cc of the 20% concentration solution with 0.078 cc of the 5% concentration solution to obtain 10 cc of an 18.5% solution.

x=9

y=-32.3