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Finding the Third Proportional to 8,412 and 19,829

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Solution

The third proportional to 8,412 and 19,829 is: 46,741.47

Step by Step Solution

  1. Step 1: Write the proportion equation
    8,412 : 19,829 = 19,829 : x
  2. Step 2: Convert to fraction form
    8,412/19,829 = 19,829/x
  3. Step 3: Cross multiply
    8,412x = 19,829 × 19,829
  4. Step 4: Simplify right side
    8,412x = 393,189,241
  5. Step 5: Solve for x
    x = 393,189,241/8,412
  6. Step 6: Final answer
    x = 46,741.47

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Why These Related Problems?

These problems maintain the same ratio (2.36) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.