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Finding the Third Proportional to 411,198 and 470,247

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Solution

The third proportional to 411,198 and 470,247 is: 537,775.58

Step by Step Solution

  1. Step 1: Write the proportion equation
    411,198 : 470,247 = 470,247 : x
  2. Step 2: Convert to fraction form
    411,198/470,247 = 470,247/x
  3. Step 3: Cross multiply
    411,198x = 470,247 × 470,247
  4. Step 4: Simplify right side
    411,198x = 221,132,241,009
  5. Step 5: Solve for x
    x = 221,132,241,009/411,198
  6. Step 6: Final answer
    x = 537,775.58

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Why These Related Problems?

These problems maintain the same ratio (1.14) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.