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Finding the Third Proportional to 301,410 and 409,356

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Solution

The third proportional to 301,410 and 409,356 is: 555,961.43

Step by Step Solution

  1. Step 1: Write the proportion equation
    301,410 : 409,356 = 409,356 : x
  2. Step 2: Convert to fraction form
    301,410/409,356 = 409,356/x
  3. Step 3: Cross multiply
    301,410x = 409,356 × 409,356
  4. Step 4: Simplify right side
    301,410x = 167,572,334,736
  5. Step 5: Solve for x
    x = 167,572,334,736/301,410
  6. Step 6: Final answer
    x = 555,961.43

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Why These Related Problems?

These problems maintain the same ratio (1.36) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.