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Finding the Third Proportional to 823.78 and 1,107.42

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Solution

The third proportional to 823.78 and 1,107.42 is: 1,488.72

Step by Step Solution

  1. Step 1: Write the proportion equation
    823.78 : 1,107.42 = 1,107.42 : x
  2. Step 2: Convert to fraction form
    823.78/1,107.42 = 1,107.42/x
  3. Step 3: Cross multiply
    823.78x = 1,107.42 × 1,107.42
  4. Step 4: Simplify right side
    823.78x = 1,226,383.21
  5. Step 5: Solve for x
    x = 1,226,383.21/823.78
  6. Step 6: Final answer
    x = 1,488.72

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Why These Related Problems?

These problems maintain the same ratio (1.34) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.