By writing and solving a system of equations, we will find that we must use 25kg of the 12% nitrogen fertilizer and 75kg of the 24% nitrogen fertilizer.
Let's define the variables:
- x = number of kg of the 24% nitrogen fertilizer.
- y = number of kg of the 12% nitrogen fertilizer.
We know that we want to get 100kg of 21% fertilizer, then we will have:
x + y = 100
And because the 100kg must be of 21% of nitrogen, we also have the equation:
x*0.24 + y*0.12 = 100*0.21
Then we have a system of two equations:
x + y = 100
x*0.24 + y*0.12 = 100*0.21
To solve this, we first isolate one variable in one of the equations, let's do it in the first one:
x = 100 - y
Now we can replace "x" in the other equation:
(100 - y)*0.24 + y*0.12 = 100*0.21
Now we can solve this for y.
(100 - y)*0.24 + y*0.12 = 100*0.21
24 + y*(0.12 - 0.24) = 21
24 - y*0.12 = 21
24 - 21 = y*0.12
3/0.12 = y = 25
Then we must use 25 kg of the 12% nitrogen fertilizer, and the other 75 kg will be of the 24% nitrogen fertilizer.
If you want to learn more, you can read:
https://brainly.com/question/9351049
