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Finding the Third Proportional to 256,864 and 409,076

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Solution

The third proportional to 256,864 and 409,076 is: 651,485.51

Step by Step Solution

  1. Step 1: Write the proportion equation
    256,864 : 409,076 = 409,076 : x
  2. Step 2: Convert to fraction form
    256,864/409,076 = 409,076/x
  3. Step 3: Cross multiply
    256,864x = 409,076 × 409,076
  4. Step 4: Simplify right side
    256,864x = 167,343,173,776
  5. Step 5: Solve for x
    x = 167,343,173,776/256,864
  6. Step 6: Final answer
    x = 651,485.51

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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.