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Finding the Third Proportional to 5,746 and 13,654

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Solution

The third proportional to 5,746 and 13,654 is: 32,445.48

Step by Step Solution

  1. Step 1: Write the proportion equation
    5,746 : 13,654 = 13,654 : x
  2. Step 2: Convert to fraction form
    5,746/13,654 = 13,654/x
  3. Step 3: Cross multiply
    5,746x = 13,654 × 13,654
  4. Step 4: Simplify right side
    5,746x = 186,431,716
  5. Step 5: Solve for x
    x = 186,431,716/5,746
  6. Step 6: Final answer
    x = 32,445.48

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Why These Related Problems?

These problems maintain the same ratio (2.38) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.