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Finding the Third Proportional to 214,194 and 470,421

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Solution

The third proportional to 214,194 and 470,421 is: 1,033,156.47

Step by Step Solution

  1. Step 1: Write the proportion equation
    214,194 : 470,421 = 470,421 : x
  2. Step 2: Convert to fraction form
    214,194/470,421 = 470,421/x
  3. Step 3: Cross multiply
    214,194x = 470,421 × 470,421
  4. Step 4: Simplify right side
    214,194x = 221,295,917,241
  5. Step 5: Solve for x
    x = 221,295,917,241/214,194
  6. Step 6: Final answer
    x = 1,033,156.47

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Why These Related Problems?

These problems maintain the same ratio (2.20) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.