Question
Real Tutor Solution
Tutor-Verified Answer
Answer
\( x = 18.5 \)
Solution
To solve the equation:
\[
\frac{8}{10} = \frac{10}{x - 6}
\]
**Step 1: Cross-Multiply**
Cross-multiplying the fractions eliminates the denominators:
\[
8 \cdot (x - 6) = 10 \cdot 10
\]
\[
8(x - 6) = 100
\]
**Step 2: Distribute the 8**
Expand the left side of the equation:
\[
8x - 48 = 100
\]
**Step 3: Isolate the Variable Term**
Add 48 to both sides to move the constant term to the right:
\[
8x = 100 + 48
\]
\[
8x = 148
\]
**Step 4: Solve for \( x \)**
Divide both sides by 8 to solve for \( x \):
\[
x = \frac{148}{8}
\]
Simplify the fraction by dividing both numerator and denominator by 4:
\[
x = \frac{37}{2} \quad \text{or} \quad x = 18.5
\]
**Final Answer:**
\[
x = 18.5
\]
Reviewed and approved by the UpStudy tutoring team
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Simplify this solution Bonus Knowledge
To solve the equation \( \frac{8}{10}=\frac{10}{x-6} \), cross-multiply to get \( 8(x-6) = 100 \). Distributing gives \( 8x - 48 = 100 \). Now add 48 to both sides to find \( 8x = 148 \), and then divide by 8 to get \( x = 18.5 \). Now let's check the world around us! Ratios and proportions are everywhere, from cooking recipes (adjusting servings) to financial planning (budgeting). Knowing how to manipulate them helps in making better decisions. Be careful with the signs! A common mistake is misplacing the negative signs when solving for \( x \) or miscalculating during cross-multiplication. It’s good to double-check each step—especially with numbers like these!
