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
?

	
H=T+Gxy

	
H=y(T−Gx)

	
H=TGx+y

	
H=T−Gxy

To isolate the variable \( H \) in the equation \( T = Gx + Hy \), we need to solve for \( H \). Here's the step-by-step process:

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

2. Subtract \( Gx \) from both sides to get \( Hy \) by itself:
   \[
   T - Gx = Hy
   \]

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

This matches the second option provided:

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

So, the correct solution is:

**\( H = \frac{T - Gx}{y} \)**

Would you like more details or have any questions? 

Here are some related questions for further exploration:

1. What happens to the value of \( H \) if \( y \) increases?
2. How would the equation change if the buckets had the same capacity?
3. Can you express \( G \) in terms of \( T \), \( x \), \( y \), and \( H \)?
4. If \( T \) is known and \( G \) and \( x \) are both zero, what would \( H \) equal?
5. How does the equation change if you add a third bucket with capacity \( z \) and filled \( K \) times?

**Tip:** When isolating a variable, remember to perform the same operation on both sides of the equation to maintain the equality.

Learn how to isolate variable H in the equation T = Gx + Hy with a step-by-step solution. This problem involves algebraic manipulation and linear equations. Suitable for students in Grades 7-9.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation