Solving the Equation: 1/8 = x/10 + y/100 + z/1000
In this article, we will delve into the world of fractions and explore the solution to the equation 1/8 = x/10 + y/100 + z/1000.
What is the Equation?
The equation 1/8 = x/10 + y/100 + z/1000 is a complex fraction equation that involves finding the values of x, y, and z. The equation is composed of four fractions: 1/8, x/10, y/100, and z/1000. Our task is to find the values of x, y, and z that satisfy the equation.
Step-by-Step Solution
To solve the equation, we can start by converting all the fractions to have a common denominator. The least common multiple (LCM) of 8, 10, 100, and 1000 is 4000. Therefore, we can convert each fraction to have a denominator of 4000:
1/8 = 500/4000 x/10 = 400x/4000 y/100 = 40y/4000 z/1000 = 4z/4000
Now, we can rewrite the equation as:
500/4000 = 400x/4000 + 40y/4000 + 4z/4000
Simplifying the Equation
To simplify the equation, we can eliminate the denominator (4000) and equate the numerators:
500 = 400x + 40y + 4z
Solving for x, y, and z
Now, we have a linear equation in three variables. To solve for x, y, and z, we need more equations. Since we only have one equation, we cannot find unique values for x, y, and z. However, we can express x, y, and z in terms of each other.
For example, we can solve for x:
x = (500 - 40y - 4z) / 400
Similarly, we can solve for y and z:
y = (500 - 400x - 4z) / 40 z = (500 - 400x - 40y) / 4
Conclusion
In conclusion, we have solved the equation 1/8 = x/10 + y/100 + z/1000 and expressed x, y, and z in terms of each other. The solution to the equation is not unique, and we need more equations to find specific values for x, y, and z.
