Question

Gabe​ Amodeo, a nuclear​ physicist, needs 80 liters of a 30​% acid solution. He currently has a 20 % solution and a 60 % solution. How many liters of each does he need to make the needed 80 liters of 30​% acid​ solution?

Answer 1

Physicist mixes 60 liters of 20 % solution is mixed with 20 liters of 60 % to get solution 80 liters of 30​% acid​ solution

Solution:

Let "x" be the liters of 20 % solution

Then, (80 - x) is the liters of 60 % solution

Final mixture is 80 liters of 30 % solution

Therefore,

"x" liters of 20 % solution and 80 - x liters of 60 % solution is mixed to get 80 liters of 30 % solution

Thus a equation is framed as:

$20 \% \times x + 60 \% \times (80-x) = 30 \% \times 80\\\\\frac{20}{100} \times x + \frac{60}{100} \times (80-x) = \frac{30}{100} \times 80\\\\0.2x + 0.6(80-x) = 24\\\\0.2x + 48 - 0.6x = 24\\\\0.4x = 24\\\\x = 60$

Thus, 60 liters of 20 % solution

Then, (80 - x) = 80 - 60 = 20

20 liters of 60 % solution