Dear beloved readers, welcome to our website! We hope your visit here brings you valuable insights and meaningful inspiration. Thank you for taking the time to stop by and explore the content we've prepared for you.
------------------------------------------------ Does [tex]\frac{x}{12} = \frac{100}{18}[/tex] also represent the situation? Explain.

To determine if the equation [tex]\(\frac{x}{12} = \frac{100}{18}\)[/tex] represents a given situation, we can solve for [tex]\(x\)[/tex] by using cross-multiplication. Here is a step-by-step solution:

1. Cross-Multiply: Start by cross-multiplying the fractions to eliminate the denominators. This gives us the equation:
[tex]\[
18 \times x = 12 \times 100
\][/tex]

2. Calculate the Right Side: Compute the multiplication on the right side:
[tex]\[
12 \times 100 = 1200
\][/tex]

3. Set Up the Equation: After computing, our equation looks like:
[tex]\[
18x = 1200
\][/tex]

4. Solve for [tex]\(x\)[/tex]: To find the value of [tex]\(x\)[/tex], divide both sides of the equation by 18:
[tex]\[
x = \frac{1200}{18}
\][/tex]

5. Compute the Division: Calculate the division to find the value of [tex]\(x\)[/tex]:
[tex]\[
x \approx 66.67
\][/tex]

6. Verification: To verify that both sides of the original equation are equal with this [tex]\(x\)[/tex], substitute [tex]\(x = 66.67\)[/tex] back into the equation and check if both sides match:
- Left side: [tex]\(\frac{66.67}{12} \approx 5.56\)[/tex]
- Right side: [tex]\(\frac{100}{18} \approx 5.56\)[/tex]

Both sides are approximately equal, confirming that our solution is accurate.

Therefore, the equation [tex]\(\frac{x}{12} = \frac{100}{18}\)[/tex] does represent the given situation, and [tex]\(x\)[/tex] is approximately 66.67.