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Finding the Third Proportional to 216,441 and 463,986

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Solution

The third proportional to 216,441 and 463,986 is: 994,649.85

Step by Step Solution

  1. Step 1: Write the proportion equation
    216,441 : 463,986 = 463,986 : x
  2. Step 2: Convert to fraction form
    216,441/463,986 = 463,986/x
  3. Step 3: Cross multiply
    216,441x = 463,986 × 463,986
  4. Step 4: Simplify right side
    216,441x = 215,283,008,196
  5. Step 5: Solve for x
    x = 215,283,008,196/216,441
  6. Step 6: Final answer
    x = 994,649.85

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Why These Related Problems?

These problems maintain the same ratio (2.14) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.