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:
[tex]x\cdot14\text{ \%+6mL}\cdot7\text{ \%=(x+6)mL}\cdot\text{8\%}[/tex]
14%=0.14
7%=0.07
8%=0.08
Now, we have to solve for x:
[tex]\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=\frac{0.06}{0.06} \\ x=1 \end{gathered}[/tex]
Let's check:
[tex]\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}[/tex]
Answer: 1 mL of the 14% medication solution is needed to make a final
