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Finding the Third Proportional to 294,138 and 414,207

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Solution

The third proportional to 294,138 and 414,207 is: 583,288.93

Step by Step Solution

  1. Step 1: Write the proportion equation
    294,138 : 414,207 = 414,207 : x
  2. Step 2: Convert to fraction form
    294,138/414,207 = 414,207/x
  3. Step 3: Cross multiply
    294,138x = 414,207 × 414,207
  4. Step 4: Simplify right side
    294,138x = 171,567,438,849
  5. Step 5: Solve for x
    x = 171,567,438,849/294,138
  6. Step 6: Final answer
    x = 583,288.93

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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.