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Finding the Third Proportional to 7,730 and 16,854

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Solution

The third proportional to 7,730 and 16,854 is: 36,747.39

Step by Step Solution

  1. Step 1: Write the proportion equation
    7,730 : 16,854 = 16,854 : x
  2. Step 2: Convert to fraction form
    7,730/16,854 = 16,854/x
  3. Step 3: Cross multiply
    7,730x = 16,854 × 16,854
  4. Step 4: Simplify right side
    7,730x = 284,057,316
  5. Step 5: Solve for x
    x = 284,057,316/7,730
  6. Step 6: Final answer
    x = 36,747.39

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Why These Related Problems?

These problems maintain the same ratio (2.18) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.