John uses a liquid fertilizer to grow flowers in his back room. His fertilizer tank has a capacity of 5 gallons and currently contains 3 gallons of fertilizer which is 10% nitrogen. If he wants to change his fertilizer to 15% nitrogen, what percentage of nitrogen should he fill his tank with?
To solve this problem, we can set up an equation based on the amount of nitrogen in the tank.
The initial amount of nitrogen in the tank is 10% of 3 gallons, which is 0.10 * 3 = 0.3 gallons.
Let's assume John needs to fill x gallons of the tank with a fertilizer that has 15% nitrogen.
With the added x gallons of 15% nitrogen fertilizer, the total amount of nitrogen in the tank will be 0.15 * x gallons.
The final amount of nitrogen in the tank must equal the desired concentration, so we can set up the equation:
0.3 + 0.15 * x = (3 + x) * y
Since the tank has a capacity of 5 gallons, the equation becomes:
0.3 + 0.15 * x = (3 + x) * 0.15
Simplifying this equation, we get:
0.3 + 0.15 * x = 0.45 + 0.15 * x
0.3 = 0.45
This equation has no solution. It means that it is not possible to change the nitrogen concentration to exactly 15% in the tank by adding extra liquid fertilizer.
To find the percentage of nitrogen John should fill his tank with, we need to determine the amount of nitrogen in the tank and the total volume of the tank.
Currently, John's tank has 3 gallons of fertilizer and the concentration of nitrogen in the fertilizer is 10%. Therefore, the amount of nitrogen in the tank is calculated by multiplying the volume of fertilizer by the concentration of nitrogen:
Nitrogen in tank = 3 gallons x 10% = 0.3 gallons
To change the fertilizer to 15% nitrogen, John needs to calculate the total volume of the tank when it is filled to capacity. Since the capacity of the tank is 5 gallons, the volume of the tank filled with fertilizer is 5 gallons.
Now, let's calculate the amount of nitrogen needed in the tank when it is filled to capacity with 15% nitrogen fertilizer.
Nitrogen needed = Total volume of tank x Desired nitrogen concentration
Since the desired nitrogen concentration is 15% and the total volume of the tank is 5 gallons, we have:
Nitrogen needed = 5 gallons x 15% = 0.75 gallons
To find the percentage of nitrogen John should fill his tank with, we divide the nitrogen needed by the total volume of the tank when it is filled to capacity:
Percentage of nitrogen to fill the tank = (Nitrogen needed / Total volume of tank) x 100
Percentage of nitrogen to fill the tank = (0.75 gallons / 5 gallons) x 100 = 15%
Therefore, John should fill his tank with fertilizer that contains 15% nitrogen in order to achieve the desired concentration.