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Finding the Third Proportional to 38,304 and 82,464

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Solution

The third proportional to 38,304 and 82,464 is: 177,535.28

Step by Step Solution

  1. Step 1: Write the proportion equation
    38,304 : 82,464 = 82,464 : x
  2. Step 2: Convert to fraction form
    38,304/82,464 = 82,464/x
  3. Step 3: Cross multiply
    38,304x = 82,464 × 82,464
  4. Step 4: Simplify right side
    38,304x = 6,800,311,296
  5. Step 5: Solve for x
    x = 6,800,311,296/38,304
  6. Step 6: Final answer
    x = 177,535.28

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Why These Related Problems?

These problems maintain the same ratio (2.15) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.