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Finding the Third Proportional to 209,048 and 407,584

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Solution

The third proportional to 209,048 and 407,584 is: 794,672.60

Step by Step Solution

  1. Step 1: Write the proportion equation
    209,048 : 407,584 = 407,584 : x
  2. Step 2: Convert to fraction form
    209,048/407,584 = 407,584/x
  3. Step 3: Cross multiply
    209,048x = 407,584 × 407,584
  4. Step 4: Simplify right side
    209,048x = 166,124,717,056
  5. Step 5: Solve for x
    x = 166,124,717,056/209,048
  6. Step 6: Final answer
    x = 794,672.60

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Why These Related Problems?

These problems maintain the same ratio (1.95) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.