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Finding the Third Proportional to 321,784 and 423,147

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Solution

The third proportional to 321,784 and 423,147 is: 556,439.67

Step by Step Solution

  1. Step 1: Write the proportion equation
    321,784 : 423,147 = 423,147 : x
  2. Step 2: Convert to fraction form
    321,784/423,147 = 423,147/x
  3. Step 3: Cross multiply
    321,784x = 423,147 × 423,147
  4. Step 4: Simplify right side
    321,784x = 179,053,383,609
  5. Step 5: Solve for x
    x = 179,053,383,609/321,784
  6. Step 6: Final answer
    x = 556,439.67

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Why These Related Problems?

These problems maintain the same ratio (1.32) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.