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Finding the Third Proportional to 21,854 and 47,678

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Solution

The third proportional to 21,854 and 47,678 is: 104,017.19

Step by Step Solution

  1. Step 1: Write the proportion equation
    21,854 : 47,678 = 47,678 : x
  2. Step 2: Convert to fraction form
    21,854/47,678 = 47,678/x
  3. Step 3: Cross multiply
    21,854x = 47,678 × 47,678
  4. Step 4: Simplify right side
    21,854x = 2,273,191,684
  5. Step 5: Solve for x
    x = 2,273,191,684/21,854
  6. Step 6: Final answer
    x = 104,017.19

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Why These Related Problems?

These problems maintain the same ratio (2.18) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.