Solving 'How Much Solution' Problems: Minoxidil Example

[Marlona Ely]

Help with one of those "how much solution to equal a percentage of acid" problems!

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My problem seems to be in just how to set up the table. Once I get the figures plugged in, I can seem to work the problem. The question asks:

Minoxidil is a drug that has recently proven to be effective in treating male pattern baldness. A pharmacist wishes to mix a solution that is 2% minoxidil. She has on hand 50 ml of a 1% solution, and she wishes to add some 4% solution to it to obtain the desired 2% solution. How much 4% solution should she add?

I've set it up like: .01 50 50(.01)
.04 x x(.04)
-02 x+50 .02(x+50)

50(.01) +x(.04) = .02(x+50)

Is this the correct way to set it up?

 

[Doc Al]

Looks good to me!

 

[M98Ranger]

Yes, you have set up the problem correctly. You have correctly identified the known quantities (50 ml of 1% solution and 4% solution to be added) and the unknown quantity (the amount of 4% solution to be added). Your setup of the table is also correct, with the concentration, volume, and total amount for each solution.

To solve the problem, you can use the equation you have set up: 50(.01) +x(.04) = .02(x+50). This equation represents the total amount of minoxidil in the final solution, which should be equal to the desired 2% concentration.

To solve for x, you can first distribute the .02 on the right side of the equation: 50(.01) + x(.04) = .02x + 1. Then, you can subtract .02x from both sides and combine like terms: 50(.01) - .02x = 1. Finally, you can divide both sides by .02 to isolate x: x = (50(.01) - 1)/.02 = 25 - 1/.02 = 25 - 50 = -25.

This means that the pharmacist would need to add -25 ml of the 4% minoxidil solution to the 50 ml of 1% solution to obtain a final solution of 2% minoxidil. However, since negative volume does not make sense, we can conclude that there is no solution to this problem. The pharmacist would need to obtain a 4% solution with a larger volume to mix with the 50 ml of 1% solution to obtain the desired 2% concentration.

I hope this helps with your understanding of how to solve "how much solution" problems. Remember to always clearly identify the known and unknown quantities, set up the table correctly, and use an equation to solve for the unknown quantity.