Solving for X in the Equation xyz 5, with y 2/5 and z 3/8

In this article, we will walk through the process of solving an algebraic equation xyz 5 given the values of y 2/5 and z 3/8. We will provide step-by-step solutions and explain the mathematical steps involved.

Given: xyz 5 y 2/5 z 3/8

Solution using Substitution Method

First, we substitute the given values of y and z into the equation: xyz 5 x * (2/5) * (3/8) 5

Now, we simplify the left-hand side of the equation. To do this, we multiply the fractions:

1 * (2/5) * (3/8) (2 * 3) / (5 * 8) 6/40 3/20

Substituting this back into the equation, we get:

x * (3/20) 5

To isolate x, we multiply both sides of the equation by the reciprocal of 3/20, which is 20/3:

x 5 * (20/3) 100/3 33.33

Verification and Simplification Steps

Let's verify the solution by substituting x 33.33, y 2/5, and z 3/8 back into the original equation:

(33.33) * (2/5) * (3/8) 5

Now, we simplify the left-hand side:

(33.33) * (2 * 3) / (5 * 8) 33.33 * (6/40) 33.33 * (3/20)

Since 33.33 is approximately 33.33, simplifying further:

33.33 * (3/20) 5

This verifies our solution.

Another Solution Method

Another approach involves directly substituting and then simplifying:

x * (2/5) * (3/8) 5

Multiplying the fractions:

x * (6/40) 5

Further simplification:

x * (3/20) 5

Multiplying both sides by 20/3:

x 5 * (20/3) 100/3 33.33

This confirms the same solution.

Further Simplification and Verification

Let's use a different set of steps to simplify and verify:

x * (2/5) * (3/8) 5

Multiplying the fractions:

x * (6/40) 5

Further simplification:

x * (3/20) 5

To isolate x, we multiply both sides by 20/3:

x 5 * (20/3) 100/3 33.33

Verification:

(33.33) * (2/5) * (3/8) 5

Simplifying:

(33.33) * (6/40) 5

(33.33) * (3/20) 5

This verifies that our final value for x is 33.33.

Conclusion: We have used multiple methods to solve the equation xyz 5, with y 2/5 and z 3/8, and obtained the same result: x 33.33.