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Finding the Third Proportional to 313,866 and 686,416

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Solution

The third proportional to 313,866 and 686,416 is: 1,501,172.24

Step by Step Solution

  1. Step 1: Write the proportion equation
    313,866 : 686,416 = 686,416 : x
  2. Step 2: Convert to fraction form
    313,866/686,416 = 686,416/x
  3. Step 3: Cross multiply
    313,866x = 686,416 × 686,416
  4. Step 4: Simplify right side
    313,866x = 471,166,925,056
  5. Step 5: Solve for x
    x = 471,166,925,056/313,866
  6. Step 6: Final answer
    x = 1,501,172.24

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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.