Question

Gave a nuclear physicist needs 60 liters of a 40% acid solution. He currently has a 20% solution and a 50% solution. How many liters of each does he need to make the needed 60 liters of 40% acid solution.

Answer 1

Let x be the number of liters of the 20% acid solution, and y be the number of liters of the 50% solution, then we can set the following system of equations:

`\begin{gathered} x+y=60 \\ x(0.20)+y(0.5)=60(0.40) \end{gathered}`

Solving the first equation for x and substituting it in the second equation we get:

`\begin{gathered} x=60-y \\ (60-y)(0.20)+0.5y=24 \\ 12-0.2y+0.5y=24 \\ 0.3y=12 \\ y=40 \end{gathered}`

Therefore x=60-40=20.

Answer: Gave must add 20 liters of the 20% solution and 40 liters of the 50% solution.