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Finding the Third Proportional to 312,101 and 471,431

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Solution

The third proportional to 312,101 and 471,431 is: 712,100.21

Step by Step Solution

  1. Step 1: Write the proportion equation
    312,101 : 471,431 = 471,431 : x
  2. Step 2: Convert to fraction form
    312,101/471,431 = 471,431/x
  3. Step 3: Cross multiply
    312,101x = 471,431 × 471,431
  4. Step 4: Simplify right side
    312,101x = 222,247,187,761
  5. Step 5: Solve for x
    x = 222,247,187,761/312,101
  6. Step 6: Final answer
    x = 712,100.21

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Why These Related Problems?

These problems maintain the same ratio (1.51) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.