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Finding the Fourth Proportional to 1,189.09, 1,780.90 and 824.14

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Solution

The fourth proportional to 1,189.09, 1,780.90 and 824.14 is: 1,234.31

Step by Step Solution

  1. Step 1: Write the proportion equation
    1,189.09 : 1,780.90 = 824.14 : x
  2. Step 2: Convert to fraction form
    1,189.09/1,780.90 = 824.14/x
  3. Step 3: Cross multiply
    1,189.09x = 1,780.90 × 824.14
  4. Step 4: Simplify right side
    1,189.09x = 1,467,710.93
  5. Step 5: Solve for x
    x = 1,467,710.93/1,189.09
  6. Step 6: Final answer
    x = 1,234.31

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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.