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Finding the Third Proportional to 31,564 and 68,024

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Solution

The third proportional to 31,564 and 68,024 is: 146,599.44

Step by Step Solution

  1. Step 1: Write the proportion equation
    31,564 : 68,024 = 68,024 : x
  2. Step 2: Convert to fraction form
    31,564/68,024 = 68,024/x
  3. Step 3: Cross multiply
    31,564x = 68,024 × 68,024
  4. Step 4: Simplify right side
    31,564x = 4,627,264,576
  5. Step 5: Solve for x
    x = 4,627,264,576/31,564
  6. Step 6: Final answer
    x = 146,599.44

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Why These Related Problems?

These problems maintain the same ratio (2.16) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.