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Finding the Fourth Proportional to 410.78, 564.05 and 409.16

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Solution

The fourth proportional to 410.78, 564.05 and 409.16 is: 561.82

Step by Step Solution

  1. Step 1: Write the proportion equation
    410.78 : 564.05 = 409.16 : x
  2. Step 2: Convert to fraction form
    410.78/564.05 = 409.16/x
  3. Step 3: Cross multiply
    410.78x = 564.05 × 409.16
  4. Step 4: Simplify right side
    410.78x = 230,781.83
  5. Step 5: Solve for x
    x = 230,781.83/410.78
  6. Step 6: Final answer
    x = 561.82

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Why These Related Problems?

These problems maintain the same ratio (1.37) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.