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Finding the Third Proportional to 257,200 and 409,272

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Solution

The third proportional to 257,200 and 409,272 is: 651,258.05

Step by Step Solution

  1. Step 1: Write the proportion equation
    257,200 : 409,272 = 409,272 : x
  2. Step 2: Convert to fraction form
    257,200/409,272 = 409,272/x
  3. Step 3: Cross multiply
    257,200x = 409,272 × 409,272
  4. Step 4: Simplify right side
    257,200x = 167,503,569,984
  5. Step 5: Solve for x
    x = 167,503,569,984/257,200
  6. Step 6: Final answer
    x = 651,258.05

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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.