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Finding the Fourth Proportional to 729.10, 1,006.10 and 414.34

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Solution

The fourth proportional to 729.10, 1,006.10 and 414.34 is: 571.76

Step by Step Solution

  1. Step 1: Write the proportion equation
    729.10 : 1,006.10 = 414.34 : x
  2. Step 2: Convert to fraction form
    729.10/1,006.10 = 414.34/x
  3. Step 3: Cross multiply
    729.10x = 1,006.10 × 414.34
  4. Step 4: Simplify right side
    729.10x = 416,867.47
  5. Step 5: Solve for x
    x = 416,867.47/729.10
  6. Step 6: Final answer
    x = 571.76

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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.