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Finding the Third Proportional to 290,024 and 408,416

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Solution

The third proportional to 290,024 and 408,416 is: 575,137.33

Step by Step Solution

  1. Step 1: Write the proportion equation
    290,024 : 408,416 = 408,416 : x
  2. Step 2: Convert to fraction form
    290,024/408,416 = 408,416/x
  3. Step 3: Cross multiply
    290,024x = 408,416 × 408,416
  4. Step 4: Simplify right side
    290,024x = 166,803,629,056
  5. Step 5: Solve for x
    x = 166,803,629,056/290,024
  6. Step 6: Final answer
    x = 575,137.33

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Why These Related Problems?

These problems maintain the same ratio (1.41) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.