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Finding the Fourth Proportional to 1,022, 1,533 and 509

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Solution

The fourth proportional to 1,022, 1,533 and 509 is: 763.50

Step by Step Solution

  1. Step 1: Write the proportion equation
    1,022 : 1,533 = 509 : x
  2. Step 2: Convert to fraction form
    1,022/1,533 = 509/x
  3. Step 3: Cross multiply
    1,022x = 1,533 × 509
  4. Step 4: Simplify right side
    1,022x = 780,297
  5. Step 5: Solve for x
    x = 780,297/1,022
  6. Step 6: Final answer
    x = 763.50

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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.