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Finding the Third Proportional to 405,144 and 537,701

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Solution

The third proportional to 405,144 and 537,701 is: 713,628.65

Step by Step Solution

  1. Step 1: Write the proportion equation
    405,144 : 537,701 = 537,701 : x
  2. Step 2: Convert to fraction form
    405,144/537,701 = 537,701/x
  3. Step 3: Cross multiply
    405,144x = 537,701 × 537,701
  4. Step 4: Simplify right side
    405,144x = 289,122,365,401
  5. Step 5: Solve for x
    x = 289,122,365,401/405,144
  6. Step 6: Final answer
    x = 713,628.65

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Why These Related Problems?

These problems maintain the same ratio (1.33) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.