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Finding the Third Proportional to 214,829 and 470,971

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Solution

The third proportional to 214,829 and 470,971 is: 1,032,512.76

Step by Step Solution

  1. Step 1: Write the proportion equation
    214,829 : 470,971 = 470,971 : x
  2. Step 2: Convert to fraction form
    214,829/470,971 = 470,971/x
  3. Step 3: Cross multiply
    214,829x = 470,971 × 470,971
  4. Step 4: Simplify right side
    214,829x = 221,813,682,841
  5. Step 5: Solve for x
    x = 221,813,682,841/214,829
  6. Step 6: Final answer
    x = 1,032,512.76

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Why These Related Problems?

These problems maintain the same ratio (2.19) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.