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Finding the Third Proportional to 418,464 and 537,296

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Solution

The third proportional to 418,464 and 537,296 is: 689,872.94

Step by Step Solution

  1. Step 1: Write the proportion equation
    418,464 : 537,296 = 537,296 : x
  2. Step 2: Convert to fraction form
    418,464/537,296 = 537,296/x
  3. Step 3: Cross multiply
    418,464x = 537,296 × 537,296
  4. Step 4: Simplify right side
    418,464x = 288,686,991,616
  5. Step 5: Solve for x
    x = 288,686,991,616/418,464
  6. Step 6: Final answer
    x = 689,872.94

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Why These Related Problems?

These problems maintain the same ratio (1.28) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.