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Finding the Third Proportional to 291,206 and 412,509

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Solution

The third proportional to 291,206 and 412,509 is: 584,341.24

Step by Step Solution

  1. Step 1: Write the proportion equation
    291,206 : 412,509 = 412,509 : x
  2. Step 2: Convert to fraction form
    291,206/412,509 = 412,509/x
  3. Step 3: Cross multiply
    291,206x = 412,509 × 412,509
  4. Step 4: Simplify right side
    291,206x = 170,163,675,081
  5. Step 5: Solve for x
    x = 170,163,675,081/291,206
  6. Step 6: Final answer
    x = 584,341.24

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Why These Related Problems?

These problems maintain the same ratio (1.42) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.