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Finding the Third Proportional to 213,040 and 464,213

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Solution

The third proportional to 213,040 and 464,213 is: 1,011,517.60

Step by Step Solution

  1. Step 1: Write the proportion equation
    213,040 : 464,213 = 464,213 : x
  2. Step 2: Convert to fraction form
    213,040/464,213 = 464,213/x
  3. Step 3: Cross multiply
    213,040x = 464,213 × 464,213
  4. Step 4: Simplify right side
    213,040x = 215,493,709,369
  5. Step 5: Solve for x
    x = 215,493,709,369/213,040
  6. Step 6: Final answer
    x = 1,011,517.60

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Why These Related Problems?

These problems maintain the same ratio (2.18) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.