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Finding the Third Proportional to 5,206 and 11,507

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Solution

The third proportional to 5,206 and 11,507 is: 25,434.32

Step by Step Solution

  1. Step 1: Write the proportion equation
    5,206 : 11,507 = 11,507 : x
  2. Step 2: Convert to fraction form
    5,206/11,507 = 11,507/x
  3. Step 3: Cross multiply
    5,206x = 11,507 × 11,507
  4. Step 4: Simplify right side
    5,206x = 132,411,049
  5. Step 5: Solve for x
    x = 132,411,049/5,206
  6. Step 6: Final answer
    x = 25,434.32

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Why These Related Problems?

These problems maintain the same ratio (2.21) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.