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Finding the Fourth Proportional to 769, 1,154.14 and 465

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Solution

The fourth proportional to 769, 1,154.14 and 465 is: 697.89

Step by Step Solution

  1. Step 1: Write the proportion equation
    769 : 1,154.14 = 465 : x
  2. Step 2: Convert to fraction form
    769/1,154.14 = 465/x
  3. Step 3: Cross multiply
    769x = 1,154.14 × 465
  4. Step 4: Simplify right side
    769x = 536,675.10
  5. Step 5: Solve for x
    x = 536,675.10/769
  6. Step 6: Final answer
    x = 697.89

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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.