Question

how many gallons of a plant food that is 9% nitrogen must be combined with another plant food that is 25% nitrogen to make 10 gal of a plant food that is 21% nitrogen?

Explanation:

Step1: Let the amount of 9% nitrogen plant - food be $x$ gallons.

Then the amount of 25% nitrogen plant - food is $(10 - x)$ gallons.

Step2: Set up the nitrogen - content equation.

The nitrogen in the 9% plant - food is $0.09x$, the nitrogen in the 25% plant - food is $0.25(10 - x)$, and the nitrogen in the final 21% plant - food (10 gallons) is $0.21\times10$. So, $0.09x+0.25(10 - x)=0.21\times10$.

Step3: Expand and simplify the equation.

$0.09x + 2.5-0.25x=2.1$. Combine like - terms: $0.09x-0.25x=2.1 - 2.5$. So, $- 0.16x=-0.4$.

Step4: Solve for $x$.

$x=\frac{-0.4}{-0.16}=2.5$.

Answer:

$2.5$