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Finding the Third Proportional to 309,684 and 678,417

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Solution

The third proportional to 309,684 and 678,417 is: 1,486,191.17

Step by Step Solution

  1. Step 1: Write the proportion equation
    309,684 : 678,417 = 678,417 : x
  2. Step 2: Convert to fraction form
    309,684/678,417 = 678,417/x
  3. Step 3: Cross multiply
    309,684x = 678,417 × 678,417
  4. Step 4: Simplify right side
    309,684x = 460,249,625,889
  5. Step 5: Solve for x
    x = 460,249,625,889/309,684
  6. Step 6: Final answer
    x = 1,486,191.17

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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.