A physician orders 3 mL of an 8% drug solution.You have only a 10% solution available.How many milliliters of 10% solution do you need to make the new 8% solution?

Question

Quizplus · Accepted Answer

Let x be the amount of 10% solution needed.

Using the equation:

0.1x + 0.1(3 - x) = 0.08(3)

Simplifying this equation produces:

0.02x = 0.06 – 0.3
0.02x = -0.24
x = -0.24/0.02 = -12

This solution must contain a negative volume of the 10% solution, which is impossible. Therefore, the only reasonable answer is to use all 3 mL of the 10% solution to make the 8% solution.

To verify this answer, we can use the equation:

0.1(3) = 0.08(x + 3)

Solving for x produces:

0.3 = 0.08x + 0.24
0.06 = 0.08x
x = 0.06/0.08 = 0.75

Therefore, we need 0.75 mL of water to make the new 8% solution. The total volume of the new solution will be 3 mL + 0.75 mL = 3.75 mL.

A Physician Orders 3 ML of an 8% Drug Solution