Two liquid fertilizer concentrates have the same density. Concentrate A is nitrogen by mass, and concentrate B is nitrogen by mass. A groundskeeper combines the two concentrates to make exactly liters of a mixture that is nitrogen by mass.
How many liters of concentrate A are used?
For mixture questions, choose one component as a baseline concentration. Find how much additional substance the target mixture needs beyond that baseline, then divide by the additional substance supplied per unit by the other component. This avoids tracking both mixture amounts separately while preserving the proportional relationship.
Hints
Define a variable
Let represent the number of liters of the concentrate. Express the amount of the concentrate using the total volume of liters.
Use decimal forms of the percentages
Rewrite the percentages as decimals. Multiply each concentrate's amount by its nitrogen decimal to represent the amount of nitrogen it contributes.
Match the total nitrogen
The combined nitrogen from both concentrates must equal the nitrogen contained in liters of the final mixture. Set those quantities equal and solve for .
Desmos Guide
Calculate the amount of concentrate A
In Desmos, enter
The numerator is the additional nitrogen needed beyond what liters of the concentrate would provide. The denominator is the additional nitrogen per liter supplied by the concentrate instead of the concentrate. Compare the displayed result with the choices.
Step-by-step Explanation
Represent the two amounts
Let be the number of liters of concentrate A. Since the total mixture is liters, the number of liters of concentrate B is .
Balance the nitrogen amounts
Write each percentage as a decimal. The nitrogen from concentrate A plus the nitrogen from concentrate B must equal the nitrogen in the final mixture:
Solve for the amount of concentrate A
Simplify the equation:
Therefore, liters of concentrate A are used, which is choice C.