The chemist has to drain 25 grams of the 20% hydrochloric acid solution and replace with the 80% solution
Solution:
Let us first set up a table and fill in the known values given
The table is attached below
Let "x" be the amount in grams for 20% acid solution
Let "y" be the amount in grams for 80% acid solution
From the given table, we can set up two equations
Sum of values of two acids = Value of mixture
0.2x + 0.8y=75
For convenience, we'll multiply the entire equation by 10,
2 x + 8 y = 750
x + 4y = 375 ------ eqn (1)
Now, Sum of amounts of each acid = Amount of mixture
x + y = 300 --------- eqn (2)
Subtracting equation (2) from (1),
( + ) x + 4 y = 375
( − ) x + y = 300
− − − − − − − −
( = ) 0 + 3y = 75
Thus, 3y = 75
y = 25
Substituting y = 25 in eqn (2),
x + 25 = 300
x = 300 – 25 = 275
So, we have x = 275 and y = 25
Here "y = 25" represents amount in grams for 80% acid solution.
We can conclude that he has to drain 25 grams of the 20% acid solution.
