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Finding the Third Proportional to 212,438 and 464,971

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Solution

The third proportional to 212,438 and 464,971 is: 1,017,699.43

Step by Step Solution

  1. Step 1: Write the proportion equation
    212,438 : 464,971 = 464,971 : x
  2. Step 2: Convert to fraction form
    212,438/464,971 = 464,971/x
  3. Step 3: Cross multiply
    212,438x = 464,971 × 464,971
  4. Step 4: Simplify right side
    212,438x = 216,198,030,841
  5. Step 5: Solve for x
    x = 216,198,030,841/212,438
  6. Step 6: Final answer
    x = 1,017,699.43

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Why These Related Problems?

These problems maintain the same ratio (2.19) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.