A druggist mixes a 10% solution of iodine with a 15% solution of iodine. How much of each solution should be used in order to obtain 20 cubic centimeters of a 12% solution?

Another algebra problem in two variables. Why are you changing names?

Please show your work for further assistance.

I'm not changing names. This is the only one that I posted today. Because this is the only one out of my homework that I don't understand how to do.

Let X = cc of 10% iodine solution

Let Y = cc of 15% iodine solution

X + Y = 20
(0.1X + 0.15 Y) = 0.12*20

X + 1.5 Y = 24
0.5Y = 4

Take it from there.

Thanx :)

To determine the amount of each solution needed, we can use a mathematical approach called the method of mixtures. Here's how you can solve it step by step:

Let's assume:
1. The amount of 10% solution used is x cubic centimeters.
2. The amount of 15% solution used is (20 - x) cubic centimeters. (As the total volume is 20 cubic centimeters.)

Now, let's calculate the amount of iodine in each solution:
1. The amount of iodine in the 10% solution is 0.10x (Since it is a 10% solution and contains 10% iodine).
2. The amount of iodine in the 15% solution is 0.15(20 - x) (As it is a 15% solution and contains 15% iodine).

The total amount of iodine in the 12% solution is: 0.12 * 20 = 2.4 cubic centimeters (Since the final solution is 12% and has 20 cubic centimeters).

Now, we can set up an equation to solve for x:
0.10x + 0.15(20 - x) = 2.4

Now, let's solve the equation:

0.10x + 3 - 0.15x = 2.4
-0.05x = -0.6
x = -0.6 / -0.05
x = 12

So, the druggist should use 12 cubic centimeters of the 10% solution and (20 - 12) = 8 cubic centimeters of the 15% solution to obtain 20 cubic centimeters of a 12% solution.