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Finding the Third Proportional to 5,854 and 10,409

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Solution

The third proportional to 5,854 and 10,409 is: 18,508.25

Step by Step Solution

  1. Step 1: Write the proportion equation
    5,854 : 10,409 = 10,409 : x
  2. Step 2: Convert to fraction form
    5,854/10,409 = 10,409/x
  3. Step 3: Cross multiply
    5,854x = 10,409 × 10,409
  4. Step 4: Simplify right side
    5,854x = 108,347,281
  5. Step 5: Solve for x
    x = 108,347,281/5,854
  6. Step 6: Final answer
    x = 18,508.25

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Why These Related Problems?

These problems maintain the same ratio (1.78) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.