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Finding the Third Proportional to 412,106 and 869,224

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Solution

The third proportional to 412,106 and 869,224 is: 1,833,388.41

Step by Step Solution

  1. Step 1: Write the proportion equation
    412,106 : 869,224 = 869,224 : x
  2. Step 2: Convert to fraction form
    412,106/869,224 = 869,224/x
  3. Step 3: Cross multiply
    412,106x = 869,224 × 869,224
  4. Step 4: Simplify right side
    412,106x = 755,550,362,176
  5. Step 5: Solve for x
    x = 755,550,362,176/412,106
  6. Step 6: Final answer
    x = 1,833,388.41

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Why These Related Problems?

These problems maintain the same ratio (2.11) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.