A pharmacist has 40% and 60% iodine solutions on hand. How many liters of each iodine solution will be required to produce 4 liters of a 50% iodine.
1. iodine1 = 2, iodine2=2
2. iodine1 = 21, iodine2 = 21
3. iodine1 = 41, iodine2 = 41
4. iodine1 = 41, iodine2 = 21
To find the amount of each iodine solution needed to produce a 50% iodine solution, we can set up a system of equations.
Let's assume x represents the amount of the 40% iodine solution (in liters) and y represents the amount of the 60% iodine solution (in liters) needed.
We have the following information:
1. The total volume of the resulting solution is 4 liters: x + y = 4.
2. The resulting solution should have a 50% iodine concentration, which means the amount of iodine in the solution should be half of the total volume. So, the amount of iodine in the solution is 0.5 * 4 = 2 liters: 0.4x + 0.6y = 2.
Now we can solve this system of equations to find the values of x and y.
Multiplying the first equation by 0.4, we get 0.4x + 0.4y = 1.6.
Subtracting this equation from the second equation, we get:
(0.4x + 0.6y) - (0.4x + 0.4y) = 2 - 1.6
0.6y - 0.4y = 0.4
0.2y = 0.4
y = 0.4 / 0.2
y = 2
Substituting the value of y back into the first equation, we can solve for x:
x + 2 = 4
x = 4 - 2
x = 2
Therefore, we need 2 liters of the 40% iodine solution and 2 liters of the 60% iodine solution to produce 4 liters of a 50% iodine solution.
So the correct answer is option 1: iodine1 = 2 liters, iodine2 = 2 liters.