00:01
For this problem, we are told that a chemist has two solutions of sulfuric acid, a 20 % solution and an 80 % solution.
00:08
We are then asked, how many of each should be used to obtain 100 liters of 62 % solution? so let's say that the number of liters of 20 % is x and the number of liters of 80 % is y.
00:21
We'd have that x plus y must be equal to 100, and we would have that 0 .2 times x plus 0 % 0 .8 times y must be equal to 0 .62.
00:35
So we can set this up as a matrix then, writing this as 1 -1 -100, 0 .2, 0 .8, 0 .62.
00:48
So the first step that we'd want to take here is to divide that second row by 0 .2, which will make that second row into, let's see here, it's 1 -1 -100 for the first row still, then the second row will become 1, 4, 3 .1.
01:05
Now we can take row 2 and subtract from it, row 1, to get 1 -100, 03, then, one second here.
01:18
Oh, excuse me, i just realized i made a silly mistake here...