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Finding the Third Proportional to 7,709 and 16,336

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Solution

The third proportional to 7,709 and 16,336 is: 34,617.32

Step by Step Solution

  1. Step 1: Write the proportion equation
    7,709 : 16,336 = 16,336 : x
  2. Step 2: Convert to fraction form
    7,709/16,336 = 16,336/x
  3. Step 3: Cross multiply
    7,709x = 16,336 × 16,336
  4. Step 4: Simplify right side
    7,709x = 266,864,896
  5. Step 5: Solve for x
    x = 266,864,896/7,709
  6. Step 6: Final answer
    x = 34,617.32

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Why These Related Problems?

These problems maintain the same ratio (2.12) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.