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Finding the Third Proportional to 294,027 and 414,065

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Solution

The third proportional to 294,027 and 414,065 is: 583,109.12

Step by Step Solution

  1. Step 1: Write the proportion equation
    294,027 : 414,065 = 414,065 : x
  2. Step 2: Convert to fraction form
    294,027/414,065 = 414,065/x
  3. Step 3: Cross multiply
    294,027x = 414,065 × 414,065
  4. Step 4: Simplify right side
    294,027x = 171,449,824,225
  5. Step 5: Solve for x
    x = 171,449,824,225/294,027
  6. Step 6: Final answer
    x = 583,109.12

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Why These Related Problems?

These problems maintain the same ratio (1.41) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.