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Finding the Fourth Proportional to 978, 1,467.54 and 465

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Solution

The fourth proportional to 978, 1,467.54 and 465 is: 697.76

Step by Step Solution

  1. Step 1: Write the proportion equation
    978 : 1,467.54 = 465 : x
  2. Step 2: Convert to fraction form
    978/1,467.54 = 465/x
  3. Step 3: Cross multiply
    978x = 1,467.54 × 465
  4. Step 4: Simplify right side
    978x = 682,406.10
  5. Step 5: Solve for x
    x = 682,406.10/978
  6. Step 6: Final answer
    x = 697.76

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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.