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Finding the Third Proportional to 294,054 and 414,102

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Solution

The third proportional to 294,054 and 414,102 is: 583,159.78

Step by Step Solution

  1. Step 1: Write the proportion equation
    294,054 : 414,102 = 414,102 : x
  2. Step 2: Convert to fraction form
    294,054/414,102 = 414,102/x
  3. Step 3: Cross multiply
    294,054x = 414,102 × 414,102
  4. Step 4: Simplify right side
    294,054x = 171,480,466,404
  5. Step 5: Solve for x
    x = 171,480,466,404/294,054
  6. Step 6: Final answer
    x = 583,159.78

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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.