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Finding the Third Proportional to 309,686 and 678,421

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Solution

The third proportional to 309,686 and 678,421 is: 1,486,199.10

Step by Step Solution

  1. Step 1: Write the proportion equation
    309,686 : 678,421 = 678,421 : x
  2. Step 2: Convert to fraction form
    309,686/678,421 = 678,421/x
  3. Step 3: Cross multiply
    309,686x = 678,421 × 678,421
  4. Step 4: Simplify right side
    309,686x = 460,255,053,241
  5. Step 5: Solve for x
    x = 460,255,053,241/309,686
  6. Step 6: Final answer
    x = 1,486,199.10

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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.