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Finding the Fourth Proportional to 1,309.76, 1,965.28 and 823.04

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Solution

The fourth proportional to 1,309.76, 1,965.28 and 823.04 is: 1,234.96

Step by Step Solution

  1. Step 1: Write the proportion equation
    1,309.76 : 1,965.28 = 823.04 : x
  2. Step 2: Convert to fraction form
    1,309.76/1,965.28 = 823.04/x
  3. Step 3: Cross multiply
    1,309.76x = 1,965.28 × 823.04
  4. Step 4: Simplify right side
    1,309.76x = 1,617,504.05
  5. Step 5: Solve for x
    x = 1,617,504.05/1,309.76
  6. Step 6: Final answer
    x = 1,234.96

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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.