Step 1 :The problem is asking for the total capacity of the container. We know that the difference between \(\frac{7}{10}\) and \(\frac{1}{2}\) of the container's capacity is 6 gallons. We can set up an equation to solve for the total capacity of the container.
Step 2 :Let's denote the total capacity of the container as C. The difference between \(\frac{7}{10}\)C and \(\frac{1}{2}\)C is 6 gallons. Therefore, we can write the equation as \(\frac{7}{10}\)C - \(\frac{1}{2}\)C = 6.
Step 3 :Solving this equation, we find that C is approximately 30 gallons.
Step 4 :Final Answer: The container can hold approximately \(\boxed{30}\) gallons.