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Finding the Fourth Proportional to 1,005.78, 1,509.35 and 457.68

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Solution

The fourth proportional to 1,005.78, 1,509.35 and 457.68 is: 686.83

Step by Step Solution

  1. Step 1: Write the proportion equation
    1,005.78 : 1,509.35 = 457.68 : x
  2. Step 2: Convert to fraction form
    1,005.78/1,509.35 = 457.68/x
  3. Step 3: Cross multiply
    1,005.78x = 1,509.35 × 457.68
  4. Step 4: Simplify right side
    1,005.78x = 690,797.02
  5. Step 5: Solve for x
    x = 690,797.02/1,005.78
  6. Step 6: Final answer
    x = 686.83

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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.