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Finding the Third Proportional to 420,342 and 578,013

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Solution

The third proportional to 420,342 and 578,013 is: 794,826.66

Step by Step Solution

  1. Step 1: Write the proportion equation
    420,342 : 578,013 = 578,013 : x
  2. Step 2: Convert to fraction form
    420,342/578,013 = 578,013/x
  3. Step 3: Cross multiply
    420,342x = 578,013 × 578,013
  4. Step 4: Simplify right side
    420,342x = 334,099,028,169
  5. Step 5: Solve for x
    x = 334,099,028,169/420,342
  6. Step 6: Final answer
    x = 794,826.66

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Why These Related Problems?

These problems maintain the same ratio (1.38) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.