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Finding the Fourth Proportional to 513.29, 707.71 and 419.83

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Solution

The fourth proportional to 513.29, 707.71 and 419.83 is: 578.85

Step by Step Solution

  1. Step 1: Write the proportion equation
    513.29 : 707.71 = 419.83 : x
  2. Step 2: Convert to fraction form
    513.29/707.71 = 419.83/x
  3. Step 3: Cross multiply
    513.29x = 707.71 × 419.83
  4. Step 4: Simplify right side
    513.29x = 297,117.89
  5. Step 5: Solve for x
    x = 297,117.89/513.29
  6. Step 6: Final answer
    x = 578.85

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Why These Related Problems?

These problems maintain the same ratio (1.38) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.