Question

A gardener has two fertilizers that contain different concentrations of Nitrogen. One has 18% Nitrogen and the other has 35% Nitrogen. How many kilograms of each should he mix to obtain 85kg of a fertilizer with 30% Nitrogen concentration?

Answer 1

The gardener needs to mix 25kg of the 18% nitrogen fertilizer with 60kg of the 35% nitrogen fertilizer to obtain 85kg of a mixture with a 30% nitrogen concentration.

Step-by-step explanation:

To solve the problem of how much of each fertilizer a gardener needs to mix to obtain 85kg of a fertilizer with a 30% Nitrogen concentration, you can apply a system of equations.

Let's define two variables:

• x = the amount of the 18% nitrogen fertilizer
• y = the amount of the 35% nitrogen fertilizer

We have two pieces of information that will lead to two equations:

1. The sum of the two fertilizers should be 85kg:
   
   x + y = 85
2. The total weight of nitrogen in the new mixture should be 30% of 85kg:
   
   0.18x + 0.35y = 0.30(85)

Solving these equations simultaneously will give us the values of x and y, the amounts of each type of fertilizer needed.

First, multiply the second equation by 100 to simplify:

18x + 35y = 30(85)

Further simplifying, we get:

18x + 35y = 2550

Now, we have the system of equations:

1. x + y = 85
2. 18x + 35y = 2550

We can solve this by substitution or elimination. Let's use the substitution method. From the first equation, we express x as x = 85 - y and replace it in the second equation:

18(85 - y) + 35y = 2550

Simplifying:

1530 - 18y + 35y = 2550

17y = 1020

y = 60kg

Now, substitute the value of y back into the first equation to find x:

x = 85 - 60 = 25kg

Therefore, the gardener needs to mix 25kg of the 18% nitrogen fertilizer with 60kg of the 35% nitrogen fertilizer.