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Finding the Third Proportional to 214,434 and 409,428

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Solution

The third proportional to 214,434 and 409,428 is: 781,738.38

Step by Step Solution

  1. Step 1: Write the proportion equation
    214,434 : 409,428 = 409,428 : x
  2. Step 2: Convert to fraction form
    214,434/409,428 = 409,428/x
  3. Step 3: Cross multiply
    214,434x = 409,428 × 409,428
  4. Step 4: Simplify right side
    214,434x = 167,631,287,184
  5. Step 5: Solve for x
    x = 167,631,287,184/214,434
  6. Step 6: Final answer
    x = 781,738.38

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Why These Related Problems?

These problems maintain the same ratio (1.91) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.