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Finding the Third Proportional to 295,678 and 463,297

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Solution

The third proportional to 295,678 and 463,297 is: 725,938.72

Step by Step Solution

  1. Step 1: Write the proportion equation
    295,678 : 463,297 = 463,297 : x
  2. Step 2: Convert to fraction form
    295,678/463,297 = 463,297/x
  3. Step 3: Cross multiply
    295,678x = 463,297 × 463,297
  4. Step 4: Simplify right side
    295,678x = 214,644,110,209
  5. Step 5: Solve for x
    x = 214,644,110,209/295,678
  6. Step 6: Final answer
    x = 725,938.72

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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.