Solving for y - xy in the Equation 1.5x 0.04y

The mathematical problem presented here involves the equation 1.5x 0.04y. This equation can be solved to find a relationship between x and y, and subsequently, we can use this relationship to solve more complex expressions such as y - xy^2. We will start by rearranging the equation to express y in terms of x.

Rearranging the Equation

Starting with the equation:

1.5x 0.04y

We can rearrange this equation to solve for y in terms of x. Doing so, we get:

y frac{1.5x}{0.04}

This can be further simplified as:

y frac{1.5}{0.04}x 37.5x

Calculating y - xy^2

Now, we need to find the value of y - xy^2. We will break this down into steps to make it more understandable.

Step 1: Calculate y - x

From the equation y 37.5x, we can now calculate y - x:

y - x 37.5x - x 36.5x

Step 2: Calculate xy^2

Next, we calculate xy^2. Since y 37.5x, we substitute this into the expression:

xy^2 x(37.5x)^2 37.5^2x^3

This simplifies to:

xy^2 1406.25x^3

Step 3: Finding the Final Expression

Now, we need to find the value of y - xy^2:

y - xy^2 36.5x - 1406.25x^3

This simplifies to:

frac{y - xy^2}{x^2} frac{36.5x - 1406.25x^3}{x^2} 36.5 cdot 37.5x 1406.25x^2

Conclusion

Therefore, the value of y - xy^2 is 1406.25x^2. This detailed breakdown not only solves the problem but also demonstrates the step-by-step process of manipulating algebraic expressions to achieve the desired result.

Related Mathematical Concepts

Understanding how to solve and manipulate equations is a fundamental skill in algebra. This type of problem involves several key concepts such as rearranging equations, substitution, and simplification of expressions. Such skills are crucial for solving more complex mathematical problems and are widely applicable in various fields of study including physics, engineering, and economics.

Further Reading

For further reading and practice, consider exploring online resources and tutorials that focus on algebraic manipulation and problem-solving techniques. These resources often provide additional examples and exercises to help solidify your understanding.