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Finding the Third Proportional to 509,649 and 714,420

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Solution

The third proportional to 509,649 and 714,420 is: 1,001,465.59

Step by Step Solution

  1. Step 1: Write the proportion equation
    509,649 : 714,420 = 714,420 : x
  2. Step 2: Convert to fraction form
    509,649/714,420 = 714,420/x
  3. Step 3: Cross multiply
    509,649x = 714,420 × 714,420
  4. Step 4: Simplify right side
    509,649x = 510,395,936,400
  5. Step 5: Solve for x
    x = 510,395,936,400/509,649
  6. Step 6: Final answer
    x = 1,001,465.59

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Why These Related Problems?

These problems maintain the same ratio (1.40) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.