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Finding the Fourth Proportional to 705.78, 1,057.86 and 513

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Solution

The fourth proportional to 705.78, 1,057.86 and 513 is: 768.91

Step by Step Solution

  1. Step 1: Write the proportion equation
    705.78 : 1,057.86 = 513 : x
  2. Step 2: Convert to fraction form
    705.78/1,057.86 = 513/x
  3. Step 3: Cross multiply
    705.78x = 1,057.86 × 513
  4. Step 4: Simplify right side
    705.78x = 542,682.18
  5. Step 5: Solve for x
    x = 542,682.18/705.78
  6. Step 6: Final answer
    x = 768.91

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Why These Related Problems?

These problems maintain the same ratio (1.50) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.