Answer :
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.
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.
