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Finding the Fourth Proportional to 465.76, 697.96 and 414.50

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Solution

The fourth proportional to 465.76, 697.96 and 414.50 is: 621.15

Step by Step Solution

  1. Step 1: Write the proportion equation
    465.76 : 697.96 = 414.50 : x
  2. Step 2: Convert to fraction form
    465.76/697.96 = 414.50/x
  3. Step 3: Cross multiply
    465.76x = 697.96 × 414.50
  4. Step 4: Simplify right side
    465.76x = 289,308.03
  5. Step 5: Solve for x
    x = 289,308.03/465.76
  6. Step 6: Final answer
    x = 621.15

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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.