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Finding the Third Proportional to 410,314 and 649,168

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Solution

The third proportional to 410,314 and 649,168 is: 1,027,064.86

Step by Step Solution

  1. Step 1: Write the proportion equation
    410,314 : 649,168 = 649,168 : x
  2. Step 2: Convert to fraction form
    410,314/649,168 = 649,168/x
  3. Step 3: Cross multiply
    410,314x = 649,168 × 649,168
  4. Step 4: Simplify right side
    410,314x = 421,419,092,224
  5. Step 5: Solve for x
    x = 421,419,092,224/410,314
  6. Step 6: Final answer
    x = 1,027,064.86

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Why These Related Problems?

These problems maintain the same ratio (1.58) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.