Description
How many gallons of a plant food that is 8% nitrogen must be combined with another plant food that is 20% nitrogen to make 10 gal of a plant food that is 17% nitrogen?
Explanation & Answer
Hello!
Denote these quantities as x and y. Then
x+y=10 (gallons).
This combination contains
0.08*x + 0.20*y of nitrogen and it must be equal to
0.17*(x+y)=0.17*10=1.7.
We obtain a linear system with two variables and two equations, solve it:
x=10-y,
0.08*(10-y)+0.2*y=1.7, or
0.8-0.08*y+0.2*y=1.7,
0.12*y=0.9,
y=0.9/0.12=90/12=30/4=7.5.
And x=10-y=2.5 (gallons).
The answer: 2.5 and 7.5 gallons, respectively.