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The given equation is:

\[
T = Gx + Hy
\]

Where:
- \(T\) is the total amount of oranges,
- \(G\) is the number of times the first bucket is filled,
- \(x\) is the capacity of the first bucket in pounds,
- \(H\) is the number of times the second bucket is filled (the variable we want to isolate),
- \(y\) is the capacity of the second bucket in pounds.

To isolate \(H\), we solve for it step by step:

1. Start with the equation:
   \[
   T = Gx + Hy
   \]

2. Subtract \(Gx\) from both sides to move it to the left-hand side:
   \[
   T - Gx = Hy
   \]

3. Finally, divide both sides by \(y\) to isolate \(H\):
   \[
   H = \frac{T - Gx}{y}
   \]

Thus, the correct solution is:

\[
H = \frac{T - Gx}{y}
\]

This corresponds to the last option in the list.

Would you like further details or have any questions?

Here are 5 follow-up questions based on this problem:
1. How would the equation change if a third bucket was added?
2. What does the variable \(Gx\) represent in the context of the problem?
3. How can this equation be applied to real-world scenarios beyond orange transportation?
4. If the weight of oranges per bucket changes, how would you adjust the equation?
5. How can you check if the solution for \(H\) is correct using specific values for \(T\), \(G\), \(x\), and \(y\)?

**Tip:** Always ensure that all terms involving the variable to be isolated are on one side of the equation before performing algebraic operations to solve for that variable.

An orange grove manager uses two different sized buckets to load oranges into a truck. The first bucket can transport x pounds of oranges, and the second bucket can transport y pounds of oranges. The first bucket is filled up G times and the second bucket is filled up H times. The total amount of oranges, T, that have been loaded can be found using the equation T = Gx + Hy. What is the solution that would correctly isolate the variable H?

Learn how to solve for H in the linear equation T = Gx + Hy. This problem involves algebraic manipulation and is suitable for students in Grades 8-10. Key formulas and step-by-step solutions are provided.

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