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Finding the Third Proportional to 212,952 and 470,211

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Solution

The third proportional to 212,952 and 470,211 is: 1,038,254.56

Step by Step Solution

  1. Step 1: Write the proportion equation
    212,952 : 470,211 = 470,211 : x
  2. Step 2: Convert to fraction form
    212,952/470,211 = 470,211/x
  3. Step 3: Cross multiply
    212,952x = 470,211 × 470,211
  4. Step 4: Simplify right side
    212,952x = 221,098,384,521
  5. Step 5: Solve for x
    x = 221,098,384,521/212,952
  6. Step 6: Final answer
    x = 1,038,254.56

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Why These Related Problems?

These problems maintain the same ratio (2.21) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.