Question

How many mL of 14% medication solution is needed to make a final solution that is a 8% medication

Answer 1

Let's call x the mL of the 14% solution that we are going to use.

Then the number of mL in the mixture will be (x+6)mL.

Thus, the equation will be:

`x\cdot14\text{ \%+6mL}\cdot7\text{ \%=(x+6)mL}\cdot\text{8\%}`

14%=0.14

7%=0.07

8%=0.08

Now, we have to solve for x:

`\begin{gathered} 0.14x+0.07\cdot6=0.08(x+6) \\ 0.14x+0.42=0.08x+0.08\cdot6 \\ 0.14x+0.42=0.08x+0.48 \\ 0.14x=0.08x+0.48-0.42 \\ 0.14x=0.08x+0.06 \\ \text{0}.14x-0.08x=0.06 \\ 0.06x=0.06 \\ x=(0.06)/(0.06) \\ x=1 \end{gathered}`

Let's check:

`\begin{gathered} 0.14\cdot1+0.07\cdot6=0.08(1+6) \\ 0.14+0.42=0.08\cdot7 \\ 0.56=0.56\text{ O.K.} \end{gathered}`

Answer: 1 mL of the 14% medication solution is needed to make a final