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Finding the Third Proportional to 13,502 and 19,821

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Solution

The third proportional to 13,502 and 19,821 is: 29,097.32

Step by Step Solution

  1. Step 1: Write the proportion equation
    13,502 : 19,821 = 19,821 : x
  2. Step 2: Convert to fraction form
    13,502/19,821 = 19,821/x
  3. Step 3: Cross multiply
    13,502x = 19,821 × 19,821
  4. Step 4: Simplify right side
    13,502x = 392,872,041
  5. Step 5: Solve for x
    x = 392,872,041/13,502
  6. Step 6: Final answer
    x = 29,097.32

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Why These Related Problems?

These problems maintain the same ratio (1.47) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.