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Finding the Third Proportional to 256,970 and 409,215

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Solution

The third proportional to 256,970 and 409,215 is: 651,659.40

Step by Step Solution

  1. Step 1: Write the proportion equation
    256,970 : 409,215 = 409,215 : x
  2. Step 2: Convert to fraction form
    256,970/409,215 = 409,215/x
  3. Step 3: Cross multiply
    256,970x = 409,215 × 409,215
  4. Step 4: Simplify right side
    256,970x = 167,456,916,225
  5. Step 5: Solve for x
    x = 167,456,916,225/256,970
  6. Step 6: Final answer
    x = 651,659.40

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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.