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Finding the Third Proportional to 431,640 and 677,117

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Solution

The third proportional to 431,640 and 677,117 is: 1,062,198.66

Step by Step Solution

  1. Step 1: Write the proportion equation
    431,640 : 677,117 = 677,117 : x
  2. Step 2: Convert to fraction form
    431,640/677,117 = 677,117/x
  3. Step 3: Cross multiply
    431,640x = 677,117 × 677,117
  4. Step 4: Simplify right side
    431,640x = 458,487,431,689
  5. Step 5: Solve for x
    x = 458,487,431,689/431,640
  6. Step 6: Final answer
    x = 1,062,198.66

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Why These Related Problems?

These problems maintain the same ratio (1.57) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.