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Finding the Third Proportional to 290,013 and 408,409

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Solution

The third proportional to 290,013 and 408,409 is: 575,139.43

Step by Step Solution

  1. Step 1: Write the proportion equation
    290,013 : 408,409 = 408,409 : x
  2. Step 2: Convert to fraction form
    290,013/408,409 = 408,409/x
  3. Step 3: Cross multiply
    290,013x = 408,409 × 408,409
  4. Step 4: Simplify right side
    290,013x = 166,797,911,281
  5. Step 5: Solve for x
    x = 166,797,911,281/290,013
  6. Step 6: Final answer
    x = 575,139.43

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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.