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Finding the Third Proportional to 514,134 and 821,016

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Solution

The third proportional to 514,134 and 821,016 is: 1,311,073.13

Step by Step Solution

  1. Step 1: Write the proportion equation
    514,134 : 821,016 = 821,016 : x
  2. Step 2: Convert to fraction form
    514,134/821,016 = 821,016/x
  3. Step 3: Cross multiply
    514,134x = 821,016 × 821,016
  4. Step 4: Simplify right side
    514,134x = 674,067,272,256
  5. Step 5: Solve for x
    x = 674,067,272,256/514,134
  6. Step 6: Final answer
    x = 1,311,073.13

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Why These Related Problems?

These problems maintain the same ratio (1.60) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.