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Finding the Third Proportional to 262,944 and 412,034

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Solution

The third proportional to 262,944 and 412,034 is: 645,658.46

Step by Step Solution

  1. Step 1: Write the proportion equation
    262,944 : 412,034 = 412,034 : x
  2. Step 2: Convert to fraction form
    262,944/412,034 = 412,034/x
  3. Step 3: Cross multiply
    262,944x = 412,034 × 412,034
  4. Step 4: Simplify right side
    262,944x = 169,772,017,156
  5. Step 5: Solve for x
    x = 169,772,017,156/262,944
  6. Step 6: Final answer
    x = 645,658.46

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Why These Related Problems?

These problems maintain the same ratio (1.57) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.