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Finding the Fourth Proportional to 2,048.14, 3,072.18 and 509.14

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Solution

The fourth proportional to 2,048.14, 3,072.18 and 509.14 is: 763.70

Step by Step Solution

  1. Step 1: Write the proportion equation
    2,048.14 : 3,072.18 = 509.14 : x
  2. Step 2: Convert to fraction form
    2,048.14/3,072.18 = 509.14/x
  3. Step 3: Cross multiply
    2,048.14x = 3,072.18 × 509.14
  4. Step 4: Simplify right side
    2,048.14x = 1,564,169.73
  5. Step 5: Solve for x
    x = 1,564,169.73/2,048.14
  6. Step 6: Final answer
    x = 763.70

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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.