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Finding the Third Proportional to 212,421 and 463,488

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Solution

The third proportional to 212,421 and 463,488 is: 1,011,298.91

Step by Step Solution

  1. Step 1: Write the proportion equation
    212,421 : 463,488 = 463,488 : x
  2. Step 2: Convert to fraction form
    212,421/463,488 = 463,488/x
  3. Step 3: Cross multiply
    212,421x = 463,488 × 463,488
  4. Step 4: Simplify right side
    212,421x = 214,821,126,144
  5. Step 5: Solve for x
    x = 214,821,126,144/212,421
  6. Step 6: Final answer
    x = 1,011,298.91

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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.