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Finding the Third Proportional to 19,786 and 29,031

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Solution

The third proportional to 19,786 and 29,031 is: 42,595.72

Step by Step Solution

  1. Step 1: Write the proportion equation
    19,786 : 29,031 = 29,031 : x
  2. Step 2: Convert to fraction form
    19,786/29,031 = 29,031/x
  3. Step 3: Cross multiply
    19,786x = 29,031 × 29,031
  4. Step 4: Simplify right side
    19,786x = 842,798,961
  5. Step 5: Solve for x
    x = 842,798,961/19,786
  6. Step 6: Final answer
    x = 42,595.72

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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.