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Finding the Third Proportional to 378,410 and 569,210

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Solution

The third proportional to 378,410 and 569,210 is: 856,214.22

Step by Step Solution

  1. Step 1: Write the proportion equation
    378,410 : 569,210 = 569,210 : x
  2. Step 2: Convert to fraction form
    378,410/569,210 = 569,210/x
  3. Step 3: Cross multiply
    378,410x = 569,210 × 569,210
  4. Step 4: Simplify right side
    378,410x = 324,000,024,100
  5. Step 5: Solve for x
    x = 324,000,024,100/378,410
  6. Step 6: Final answer
    x = 856,214.22

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Why These Related Problems?

These problems maintain the same ratio (1.50) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.