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Finding the Third Proportional to 782.25 and 1,542.75

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Solution

The third proportional to 782.25 and 1,542.75 is: 3,042.60

Step by Step Solution

  1. Step 1: Write the proportion equation
    782.25 : 1,542.75 = 1,542.75 : x
  2. Step 2: Convert to fraction form
    782.25/1,542.75 = 1,542.75/x
  3. Step 3: Cross multiply
    782.25x = 1,542.75 × 1,542.75
  4. Step 4: Simplify right side
    782.25x = 2,380,077.56
  5. Step 5: Solve for x
    x = 2,380,077.56/782.25
  6. Step 6: Final answer
    x = 3,042.60

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Why These Related Problems?

These problems maintain the same ratio (1.97) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.