91Ó°ÊÓ

When solving percentage problems in mathematics, forming and solving equations becomes an essential skill. In this context, the problem provides us with certain known values that we need to use to solve for an unknown quantity. This requires setting up an equation that reflects the situation described.

For our exercise, the percentage is given as 10%. The desalination plant provides 50 million gallons, which is 10% of the total water supply for San Diego County. To form the equation, we translate '10% of the total supply' into a mathematical expression:

• Let the total water supply be denoted by the variable \( x \).
• 10% of \( x \) becomes \( 0.10x \).
• We know \( 0.10x = 50 \).

This equation models the situation using a mathematical representation. Solving this equation involves isolating \( x \) by dividing both sides by 0.10, resulting in \( x = 500 \). This tells us that the total water supply is 500 million gallons per day.

Equation solving is critical in interpreting complex problems by breaking them down into simple mathematical operations that lead us to our solution.

Water desalination is a process used to remove salt and other impurities from seawater to produce fresh drinking water. This process is vital in regions with limited access to freshwater sources. In our exercise, a new desalination plant is considered crucial for providing 50 million gallons of drinkable water each day to San Diego County.

The importance of such plants can be highlighted as follows:

• Desalination provides a reliable source of water, crucial in areas facing water scarcity.
• It helps in reducing dependency on external or natural water sources that may not be as reliable.
• Plants like the one in Carlsbad contribute significantly to a region's total water supply.
• It helps in sustaining the agricultural and urban demands by ensuring a steady supply of fresh water.

By ensuring a consistent water supply, desalination plays a fundamental role in supporting the region’s infrastructure, especially in water-stressed areas.

Mathematical interpretation transforms real-world scenarios into mathematical equations that can easily be solved. In this exercise, mathematical interpretation helps us in understanding the impact of the desalination plant on San Diego County's water supply.

Interpretation involves the following steps:

• Identifying known values like the amount provided by the plant and its percentage.
• Formulating equations based on these values to find unknown quantities.
• Understanding how the result contextualizes the problem situation.

In our exercise, interpreting the answer, 500 million gallons, shows how much water the entire county consumes daily. This interpretation informs us about the scale of water provision managed by city planners. Mathematical interpretation not only allows for the solution of algebraic equations but also gives insight into how solutions apply in real-world contexts, ensuring practical applications of math.