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Finding the Third Proportional to 261,784 and 420,011

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Solution

The third proportional to 261,784 and 420,011 is: 673,873.27

Step by Step Solution

  1. Step 1: Write the proportion equation
    261,784 : 420,011 = 420,011 : x
  2. Step 2: Convert to fraction form
    261,784/420,011 = 420,011/x
  3. Step 3: Cross multiply
    261,784x = 420,011 × 420,011
  4. Step 4: Simplify right side
    261,784x = 176,409,240,121
  5. Step 5: Solve for x
    x = 176,409,240,121/261,784
  6. Step 6: Final answer
    x = 673,873.27

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Why These Related Problems?

These problems maintain the same ratio (1.60) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.