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Finding the Third Proportional to 31,562 and 40,214

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Solution

The third proportional to 31,562 and 40,214 is: 51,237.75

Step by Step Solution

  1. Step 1: Write the proportion equation
    31,562 : 40,214 = 40,214 : x
  2. Step 2: Convert to fraction form
    31,562/40,214 = 40,214/x
  3. Step 3: Cross multiply
    31,562x = 40,214 × 40,214
  4. Step 4: Simplify right side
    31,562x = 1,617,165,796
  5. Step 5: Solve for x
    x = 1,617,165,796/31,562
  6. Step 6: Final answer
    x = 51,237.75

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Why These Related Problems?

These problems maintain the same ratio (1.27) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.