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Finding the Third Proportional to 7,834 and 8,654

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Solution

The third proportional to 7,834 and 8,654 is: 9,559.83

Step by Step Solution

  1. Step 1: Write the proportion equation
    7,834 : 8,654 = 8,654 : x
  2. Step 2: Convert to fraction form
    7,834/8,654 = 8,654/x
  3. Step 3: Cross multiply
    7,834x = 8,654 × 8,654
  4. Step 4: Simplify right side
    7,834x = 74,891,716
  5. Step 5: Solve for x
    x = 74,891,716/7,834
  6. Step 6: Final answer
    x = 9,559.83

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Why These Related Problems?

These problems maintain the same ratio (1.10) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.