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Finding the Fourth Proportional to 523.35, 783 and 414

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Solution

The fourth proportional to 523.35, 783 and 414 is: 619.40

Step by Step Solution

  1. Step 1: Write the proportion equation
    523.35 : 783 = 414 : x
  2. Step 2: Convert to fraction form
    523.35/783 = 414/x
  3. Step 3: Cross multiply
    523.35x = 783 × 414
  4. Step 4: Simplify right side
    523.35x = 324,162
  5. Step 5: Solve for x
    x = 324,162/523.35
  6. Step 6: Final answer
    x = 619.40

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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.