A pharmacist wishes to mix a solution that is 7​% Minoxidil. She has on hand 70 ml of a 5​% solution and wishes to add some 9​% solution to obtain the desired 7​% solution. How much 9​% solution should she​ add?

Answer 1

To solve this problem, we can use a mixture equation where we let \( x \) be the amount of the 9% Minoxidil solution to be added (in ml).

We know the following:

• The pharmacist has 70 ml of a 5% solution.
• The final solution needs to be 7%, and it will consist of the 70 ml of the 5% solution and \( x \) ml of the 9% solution.

First, let's calculate the total amount of Minoxidil in each solution:

1. Amount of Minoxidil in the 5% solution: \[ 0.05 \times 70 = 3.5 \text{ ml} \]

2. Amount of Minoxidil in the 9% solution (which we don't know yet since we are adding \( x \)): \[ 0.09 \times x \]

Now, we can set up an equation for the total concentration of the mixed solution. The total volume of the mixed solution will be \( 70 + x \) ml, and we want this solution to be 7% Minoxidil:

\[ \frac{3.5 + 0.09x}{70 + x} = 0.07 \]

Next, cross-multiply to eliminate the fraction:

\[ 3.5 + 0.09x = 0.07(70 + x) \]

Now, distribute the 0.07:

\[ 3.5 + 0.09x = 4.9 + 0.07x \]

Now, isolate \( x \) by moving the terms involving \( x \) to one side and constant terms to the other:

\[ 3.5 - 4.9 = 0.07x - 0.09x \]

Simplifying this gives:

\[ -1.4 = -0.02x \]

Now, solve for \( x \):

\[ x = \frac{-1.4}{-0.02} = 70 \]

So, the pharmacist should add 70 ml of the 9% solution to obtain a mixture that is 7% Minoxidil.