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Finding the Fourth Proportional to 1,187.10, 1,780.19 and 820.78

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Solution

The fourth proportional to 1,187.10, 1,780.19 and 820.78 is: 1,230.85

Step by Step Solution

  1. Step 1: Write the proportion equation
    1,187.10 : 1,780.19 = 820.78 : x
  2. Step 2: Convert to fraction form
    1,187.10/1,780.19 = 820.78/x
  3. Step 3: Cross multiply
    1,187.10x = 1,780.19 × 820.78
  4. Step 4: Simplify right side
    1,187.10x = 1,461,144.35
  5. Step 5: Solve for x
    x = 1,461,144.35/1,187.10
  6. Step 6: Final answer
    x = 1,230.85

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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.