Solving Algebraic Equations for X/Y and X/Z

In this article, we explore the problem of solving algebraic equations to find the values of X/Y and X/Z. By using the given information and applying basic algebraic operations, we can find the solution more effectively. Let's break down the given information:

We have two equations:

X/Y 60 Z/Y 3

Step-by-Step Solution

First, we express Z in terms of Y using the second equation:

Given the equation:

Z/Y 3

We can rewrite this as:

Z 3Y

Now, let's find the value of X/Z. We know that:

X/Z X/Y ÷ (Z/Y)

Substitute the given values:

X/Z 60 ÷ 3 20

Now, we can add the two values:

X/Y X/Z 60 20 80

Another Method to Solve the Equations

We can also solve the equations in another way by directly substituting the expressions:

Given:

X/Y 60

Z/Y 3

We express X and Z in terms of Y:

From the first equation:

X 60Y

From the second equation:

Z 3Y

We substitute these expressions to find:

X/Z 60Y / 3Y 20

Therefore:

X/Y X/Z 60 20 80

Revisiting the Equations in a General Form

We can also solve the equations by expressing X/Z directly:

Given:

X/Y 60

Z/Y 3

We rewrite the relationship between X and Z:

X/Z X/Y ÷ (Z/Y)

Substitute the values:

X/Z 60 ÷ 3 20

Adding the values:

X/Y X/Z 60 20 80

Conclusion

In this article, we have explored how to solve the algebraic equation to find the value of X/Y X/Z. By using the given values and basic algebraic operations, we were able to arrive at the final answer of 80. This solution demonstrates the importance of understanding algebraic relationships and how they can be manipulated to find the desired result.

Further Reading

If you're interested in learning more about algebraic equations and problem-solving techniques, consider checking the following resources:

Introduction to Algebraic Equations Basic Algebraic Operations Problem-Solving Strategies in Mathematics