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Finding the Third Proportional to 291,224 and 447,009

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Solution

The third proportional to 291,224 and 447,009 is: 686,128.36

Step by Step Solution

  1. Step 1: Write the proportion equation
    291,224 : 447,009 = 447,009 : x
  2. Step 2: Convert to fraction form
    291,224/447,009 = 447,009/x
  3. Step 3: Cross multiply
    291,224x = 447,009 × 447,009
  4. Step 4: Simplify right side
    291,224x = 199,817,046,081
  5. Step 5: Solve for x
    x = 199,817,046,081/291,224
  6. Step 6: Final answer
    x = 686,128.36

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Why These Related Problems?

These problems maintain the same ratio (1.53) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.