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Finding the Third Proportional to 257,196 and 409,266

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Solution

The third proportional to 257,196 and 409,266 is: 651,249.08

Step by Step Solution

  1. Step 1: Write the proportion equation
    257,196 : 409,266 = 409,266 : x
  2. Step 2: Convert to fraction form
    257,196/409,266 = 409,266/x
  3. Step 3: Cross multiply
    257,196x = 409,266 × 409,266
  4. Step 4: Simplify right side
    257,196x = 167,498,658,756
  5. Step 5: Solve for x
    x = 167,498,658,756/257,196
  6. Step 6: Final answer
    x = 651,249.08

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Why These Related Problems?

These problems maintain the same ratio (1.59) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.