An aquifer receives $40 m^3$ of precipitation and loses $10 m^3$ of water through natural movement. How much water can be pumped from the aquifer to balance the budget?
A. $10 m^3$
B. $20 m^3$
C. $30 m^3$
D. $40 m^3
Answer (2)
Define variables: P = 40 m 3 (precipitation), L = 10 m 3 (natural loss), and X (water pumped).
Set up the equation to balance the budget: P = L + X .
Solve for X : X = P − L .
Substitute the values and calculate: X = 40 m 3 − 10 m 3 = 30 m 3 .
Explanation
Understanding the Problem We are given that an aquifer receives 40 m 3 of precipitation and loses 10 m 3 of water through natural movement. We need to find out how much water can be pumped from the aquifer to balance the budget.
Defining Variables Let P be the amount of precipitation the aquifer receives, which is 40 m 3 . Let L be the amount of water the aquifer loses through natural movement, which is 10 m 3 . Let X be the amount of water that can be pumped from the aquifer to balance the budget.
Setting up the Equation To balance the budget, the amount of water coming in must equal the amount of water going out. Therefore, we have the equation: P = L + X
Solving for X We want to solve for X , the amount of water that can be pumped out. We can rearrange the equation to isolate X : X = P − L
Substituting Values Now, we substitute the given values into the equation: X = 40 m 3 − 10 m 3
Calculating the Answer Calculating the value of X , we get: X = 30 m 3 Therefore, 30 m 3 of water can be pumped from the aquifer to balance the budget.
Examples
Imagine you're managing a water reservoir. The problem we solved is similar to balancing the water input (precipitation) with the water output (natural loss and pumping). If you know how much water comes in and how much is naturally lost, you can calculate how much water you can safely pump out without depleting the reservoir. This ensures a sustainable water supply for the community.
To balance the water budget of the aquifer, 30 m 3 of water can be pumped out without depleting its resources, given that it receives 40 m 3 of precipitation and loses 10 m 3 through natural movement. The final answer is therefore option C: 30 m 3 .
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