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Finding the Third Proportional to 823.61 and 1,294.42

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Solution

The third proportional to 823.61 and 1,294.42 is: 2,034.37

Step by Step Solution

  1. Step 1: Write the proportion equation
    823.61 : 1,294.42 = 1,294.42 : x
  2. Step 2: Convert to fraction form
    823.61/1,294.42 = 1,294.42/x
  3. Step 3: Cross multiply
    823.61x = 1,294.42 × 1,294.42
  4. Step 4: Simplify right side
    823.61x = 1,675,517.88
  5. Step 5: Solve for x
    x = 1,675,517.88/823.61
  6. Step 6: Final answer
    x = 2,034.37

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Why These Related Problems?

These problems maintain the same ratio (1.57) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.