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Finding the Third Proportional to 420,512 and 972,496

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Solution

The third proportional to 420,512 and 972,496 is: 2,249,040.38

Step by Step Solution

  1. Step 1: Write the proportion equation
    420,512 : 972,496 = 972,496 : x
  2. Step 2: Convert to fraction form
    420,512/972,496 = 972,496/x
  3. Step 3: Cross multiply
    420,512x = 972,496 × 972,496
  4. Step 4: Simplify right side
    420,512x = 945,748,470,016
  5. Step 5: Solve for x
    x = 945,748,470,016/420,512
  6. Step 6: Final answer
    x = 2,249,040.38

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Why These Related Problems?

These problems maintain the same ratio (2.31) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.