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Finding the Third Proportional to 4,190 and 9,746

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Solution

The third proportional to 4,190 and 9,746 is: 22,669.34

Step by Step Solution

  1. Step 1: Write the proportion equation
    4,190 : 9,746 = 9,746 : x
  2. Step 2: Convert to fraction form
    4,190/9,746 = 9,746/x
  3. Step 3: Cross multiply
    4,190x = 9,746 × 9,746
  4. Step 4: Simplify right side
    4,190x = 94,984,516
  5. Step 5: Solve for x
    x = 94,984,516/4,190
  6. Step 6: Final answer
    x = 22,669.34

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Why These Related Problems?

These problems maintain the same ratio (2.33) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.