(106.359)/(x+106.359)*100=60.5 solve for x with steps

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!

Learn how to solve the rational equation (106.359)/(x+106.359)*100 = 60.5 with step-by-step guidance. This problem covers key algebraic concepts such as rational equations and percentages, making it suitable for students in Grades 8-10.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation