00:01
Okay, so for this problem, the method, the approach i used was really some guess and check.
00:07
But from the background information, right, they tell us that a mixture of seven pounds of fertilizer a, 21 pounds of fertilizer b, and eight pounds of fertilizer c is the optimum, right? that's the ratio that we want for optimal nutrients for our plant.
00:25
They then tell us, right, that commercial brand x contains equal parts fertilizer b and c.
00:31
So i just kind of wrote on a little equation here, x equals b plus c.
00:36
Commercial brand y contains one part a and two parts fertilizer b.
00:41
So i wrote another equation.
00:42
Y equals a plus 2b.
00:45
And then lastly, commercial brand z contains two parts fertilizer a, five parts fertilizer b, and two parts of fertilizer c.
00:55
How much of each fertilizer brand is needed to obtain the desired mixture.
01:00
So like i said, i really did a lot of guess and check, just kind of putting different coefficients, different amounts with brand x, brand y, and brand z to see what they came out to.
01:10
And what i discovered was that when you get one pound, right, one pound of brand z, so times one, what you will end up with is two pounds of a, five pounds of b and two pounds of c, right? all my little coefficients there stay the same.
01:42
So then i kind of thought about a.
01:44
I know that we need seven pounds of a.
01:46
The only other equation that involves a is this one right here.
01:50
And so to get the seven, i've already got two right here...