We are given the equation:

$\frac{106.359}{x + 106.359} \times 100 = 60.5$

To solve for $x$, let's proceed step by step.

Step 1: Eliminate the 100 multiplier.

Divide both sides of the equation by 100 to remove the percentage:

$\frac{106.359}{x + 106.359} = \frac{60.5}{100} = 0.605$

Now the equation becomes:

$\frac{106.359}{x + 106.359} = 0.605$

Step 2: Isolate the denominator.

Multiply both sides of the equation by $(x + 106.359)$ to get rid of the fraction:

$106.359 = 0.605 \times (x + 106.359)$

Step 3: Expand the right-hand side.

Distribute the 0.605 on the right-hand side:

$106.359 = 0.605x + 0.605 \times 106.359$

$106.359 = 0.605x + 64.349395$

Step 4: Isolate the $x$-term.

Subtract $64.349395$ from both sides:

$106.359 - 64.349395 = 0.605x$

$42.009605 = 0.605x$

Step 5: Solve for $x$.

Now, divide both sides by 0.605 to get $x$:

$x = \frac{42.009605}{0.605}$

$x \approx 69.45$

So, the solution is approximately:

$x \approx 69.45$

Would you like any further details or explanations?

5 Related Questions:

1. How would the solution change if the percentage was different?
2. Can you solve similar problems with other percentages?
3. How does the equation change if you had $106.359 + x$ in the denominator instead of $x + 106.359$?
4. What if we had $60.5\%$ in decimal form from the start?
5. How does solving rational equations like this apply in real-world scenarios?

Tip:

Always double-check units when solving equations involving percentages to ensure correct interpretation of the problem!