A fuel oil distributor has 120,000 gallons of fuel with 0.9...

A fuel oil distributor has 120,000 gallons of fuel with $0.9 \%$ sulfur content, which exceeds pollution control standards of $0.8 \%$ sulfur content. How many gallons of fuel oil with a $0.3 \%$ sulfur content must be added to the 120,000 gallons to obtain fuel oil that will comply with the pollution control standards?

Key Concepts

Conservation of Components

The conservation of components concept states that the total amount of a particular substance in a final mixture is equal to the sum of the amounts present in the individual components. In this context, accounting for the total sulfur content before and after mixing is essential to determining how much of a second fuel must be added.

Linear Equation Setup and Solving

Setting up and solving a linear equation is a fundamental approach in problems involving mixtures. By equating the total amount of the component from each source to the amount required in the final mixture, one can form an equation that, when solved, reveals the unknown quantity needed to achieve the desired concentration.

Mixture Problems

Mixture problems involve combining substances that have different concentrations or properties in order to obtain a final mixture that meets a specific criterion. These problems require understanding how the different parts contribute to the overall mixture and ensuring that the desired balance is achieved.

Weighted Averages

Weighted averages play a critical role in mixing substance problems because they allow for the calculation of the overall concentration based on the contributions of each component. This involves multiplying each component's concentration by its proportion in the mix and then summing the results to find the overall average.

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