Let's go through each step of your work to identify where the mistake might be.

1. Original Equation: $\frac{1}{60}x + \frac{1}{40}(50 - x) = 1$

2. Finding a Common Denominator: To solve this equation, it’s best to clear the fractions by finding a common multiple for 60 and 40, which is 120. Multiply each term by 120: $120 \cdot \frac{1}{60}x + 120 \cdot \frac{1}{40}(50 - x) = 120 \cdot 1$ Simplifying each term: $2x + 3(50 - x) = 120$

3. Expanding and Simplifying: Expanding $3(50 - x)$: $2x + 150 - 3x = 120$ Combine like terms: $-x + 150 = 120$ Isolate $x$ by moving constants: $-x = -30$ Thus, $x = 30$.

Explanation of the Mistake

In your steps, it looks like you complicated the approach with multiple conversions and over-expanded terms, which led to unnecessary complexity. This may have caused the incorrect values in the final calculations.

Would you like additional explanation on these steps, or help with similar equations?

Related Questions

1. How do you solve linear equations with fractions more systematically?
2. What is a common denominator, and why is it useful for solving equations?
3. How can you verify your solution in a fraction equation?
4. What methods can simplify complex algebraic steps?
5. How does clearing fractions help in solving real-life rate problems?

Tip

When working with fractions in equations, always consider multiplying through by the least common multiple to eliminate denominators and simplify your calculations.