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Finding the Third Proportional to 309,724 and 678,464

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Solution

The third proportional to 309,724 and 678,464 is: 1,486,205.14

Step by Step Solution

  1. Step 1: Write the proportion equation
    309,724 : 678,464 = 678,464 : x
  2. Step 2: Convert to fraction form
    309,724/678,464 = 678,464/x
  3. Step 3: Cross multiply
    309,724x = 678,464 × 678,464
  4. Step 4: Simplify right side
    309,724x = 460,313,399,296
  5. Step 5: Solve for x
    x = 460,313,399,296/309,724
  6. Step 6: Final answer
    x = 1,486,205.14

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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.