Answer:
700 ml of Solution B was used
Explanation:
Whenever we have unknowns the first thing to do is to represent the unknowns using variables, set up equations using given information and solve equations for the unknowns
Here the unknowns are volume of solution A and volume of solution B
Set up our variables as follows
Let x = volume of solution A used for mixing in ml
Let y = volume of solution B used for mixing in ml
We are given that volume of A used is 400 ml less than volume of B used
In math terms this can be represented as
y - x = 400
Or,
- x + y = 400 [1]
We are given the percentages of alcohol in A and B respectively
Since A contains 12% alcohol, the actual volume of alcohol in A
= 12% of x ml
= 0.12x (12% = 12/100 = 0.12)
Similarly alcohol by volume in B
= 0.20x
Total alcohol by volume if x of A and y of B are mixed is
0.12x + 0.20y
and we are given that this quantity is 176 ml
So we set up our second equation as
0.12x + 0.20y = 176 [2]
Using both equations we eliminate either the x or y terms to arrive at an equation involving only the other term.
Since the question asks us to determine only the volume of Solution B used, we should eliminate x term from both equations to get a single equation involving only the y term
Let's review the equations:
- x + y = 400 [1]
0.12x + 0.20y = 176 [2]
Make the coefficients of x the same :
Multiply [1] by 0.12
=> -0.12x + 0.12y = = 0.12 x 400
=> 0.12x + 0.12y = 48 [3]
Add [2] and [3] to eliminate the x term
0.12x + 0.20y = 176
+
-0.12x + 0.12y = 48
-----------------------------------------
0x + 0.32 y = 224
=> 0,32y = 224
Divide both sides by 0.32
==> 0.32y/0.32 = 224/0.32
==> y = 700
So 700 ml of Solution B was used
If we wanted to find volume of solution A used, subtract 400 from 700 to get 300 ml of A