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Finding the Third Proportional to 305,742 and 463,230

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Solution

The third proportional to 305,742 and 463,230 is: 701,840.22

Step by Step Solution

  1. Step 1: Write the proportion equation
    305,742 : 463,230 = 463,230 : x
  2. Step 2: Convert to fraction form
    305,742/463,230 = 463,230/x
  3. Step 3: Cross multiply
    305,742x = 463,230 × 463,230
  4. Step 4: Simplify right side
    305,742x = 214,582,032,900
  5. Step 5: Solve for x
    x = 214,582,032,900/305,742
  6. Step 6: Final answer
    x = 701,840.22

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Why These Related Problems?

These problems maintain the same ratio (1.52) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.