Answer:
The technician need to combine 12-liter of pure acid and 36-liter of 20% acid to make a 48-liter of a 40% acid solution.
Step-by-step explanation:
To find the volume of each batch of acid, we can create a system of equations.
Let:
- \(x\) = volume of the pure acid (100%)
- \(y\) = volume of the 20% acid
Given:
(a) the solution volume = 48-liter
This means the total volume of the 100% acid and the 20% acid equals to 48-liter:
\(x+y=48\ ...\ [1]\)
(b) the acid volume = 40% × 48-liter
This means the total acid of the 100% acid and the 20% acid equals to 40% × 48-liter:
\(100\%\times x+20\%\times y=40\%\times48\)
\(x+0.2y=19.2\ ...\ [2]\)
By combining [1] & [2]:
\(x+y=48\)
\(x+0.2y=19.2\)
---------------------- (-)
\(0.8y=28.8\)
\(y=36\)
By substituting \(y=36\) into [1]:
\(x+y=48\)
\(x+36=38\)
\(x=12\)
Hence, the technician need to combine 12-liter of pure acid and 36-liter of 20% acid.