An orange grove manager uses two different sized buckets to load oranges into a truck.  The first bucket can transport  x
 pound 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
?

To isolate the variable \( H \) in the equation \( T = Gx + Hy \), you need to solve for \( H \) by following these steps:

1. **Subtract \( Gx \) from both sides**:
   \[
   T - Gx = Hy
   \]

2. **Divide both sides by \( y \)**:
   \[
   H = \frac{T - Gx}{y}
   \]

So, the solution that correctly isolates the variable \( H \) is:
\[
H = \frac{T - Gx}{y}
\]

Would you like more details or have any questions?

Here are five related questions to consider:
1. How would you isolate \( G \) instead of \( H \) in the equation?
2. What happens to \( H \) if \( y \) is zero?
3. How can this equation be used in a real-world scenario?
4. What assumptions are made in this equation regarding the buckets?
5. How would you graph the relationship between \( T \) and \( H \)?

**Tip:** When isolating variables, always perform the same operation on both sides of the equation to maintain equality.

Learn how to isolate the variable H in a linear equation T = Gx + Hy step-by-step with a detailed solution. This problem covers key algebraic concepts including the isolation of variables and is suitable for students in Grades 7-9.

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