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Finding the Fourth Proportional to 2,051.78, 3,077.64 and 512.78

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Solution

The fourth proportional to 2,051.78, 3,077.64 and 512.78 is: 769.17

Step by Step Solution

  1. Step 1: Write the proportion equation
    2,051.78 : 3,077.64 = 512.78 : x
  2. Step 2: Convert to fraction form
    2,051.78/3,077.64 = 512.78/x
  3. Step 3: Cross multiply
    2,051.78x = 3,077.64 × 512.78
  4. Step 4: Simplify right side
    2,051.78x = 1,578,159.93
  5. Step 5: Solve for x
    x = 1,578,159.93/2,051.78
  6. Step 6: Final answer
    x = 769.17

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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.