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Finding the Third Proportional to 31,540 and 46,206

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Solution

The third proportional to 31,540 and 46,206 is: 67,691.64

Step by Step Solution

  1. Step 1: Write the proportion equation
    31,540 : 46,206 = 46,206 : x
  2. Step 2: Convert to fraction form
    31,540/46,206 = 46,206/x
  3. Step 3: Cross multiply
    31,540x = 46,206 × 46,206
  4. Step 4: Simplify right side
    31,540x = 2,134,994,436
  5. Step 5: Solve for x
    x = 2,134,994,436/31,540
  6. Step 6: Final answer
    x = 67,691.64

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Why These Related Problems?

These problems maintain the same ratio (1.46) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.