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Finding the Third Proportional to 13,038 and 19,507

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Solution

The third proportional to 13,038 and 19,507 is: 29,185.69

Step by Step Solution

  1. Step 1: Write the proportion equation
    13,038 : 19,507 = 19,507 : x
  2. Step 2: Convert to fraction form
    13,038/19,507 = 19,507/x
  3. Step 3: Cross multiply
    13,038x = 19,507 × 19,507
  4. Step 4: Simplify right side
    13,038x = 380,523,049
  5. Step 5: Solve for x
    x = 380,523,049/13,038
  6. Step 6: Final answer
    x = 29,185.69

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Why These Related Problems?

These problems maintain the same ratio (1.50) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.