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Finding the Fourth Proportional to 566, 781.50 and 419

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Solution

The fourth proportional to 566, 781.50 and 419 is: 578.53

Step by Step Solution

  1. Step 1: Write the proportion equation
    566 : 781.50 = 419 : x
  2. Step 2: Convert to fraction form
    566/781.50 = 419/x
  3. Step 3: Cross multiply
    566x = 781.50 × 419
  4. Step 4: Simplify right side
    566x = 327,448.50
  5. Step 5: Solve for x
    x = 327,448.50/566
  6. Step 6: Final answer
    x = 578.53

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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.