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Finding the Third Proportional to 206,784 and 311,904

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Solution

The third proportional to 206,784 and 311,904 is: 470,462.44

Step by Step Solution

  1. Step 1: Write the proportion equation
    206,784 : 311,904 = 311,904 : x
  2. Step 2: Convert to fraction form
    206,784/311,904 = 311,904/x
  3. Step 3: Cross multiply
    206,784x = 311,904 × 311,904
  4. Step 4: Simplify right side
    206,784x = 97,284,105,216
  5. Step 5: Solve for x
    x = 97,284,105,216/206,784
  6. Step 6: Final answer
    x = 470,462.44

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Why These Related Problems?

These problems maintain the same ratio (1.51) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.