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Finding the Third Proportional to 7,706 and 16,506

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Solution

The third proportional to 7,706 and 16,506 is: 35,355.31

Step by Step Solution

  1. Step 1: Write the proportion equation
    7,706 : 16,506 = 16,506 : x
  2. Step 2: Convert to fraction form
    7,706/16,506 = 16,506/x
  3. Step 3: Cross multiply
    7,706x = 16,506 × 16,506
  4. Step 4: Simplify right side
    7,706x = 272,448,036
  5. Step 5: Solve for x
    x = 272,448,036/7,706
  6. Step 6: Final answer
    x = 35,355.31

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Why These Related Problems?

These problems maintain the same ratio (2.14) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.