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Finding the Fourth Proportional to 1,309.85, 1,965.23 and 822.32

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Solution

The fourth proportional to 1,309.85, 1,965.23 and 822.32 is: 1,233.76

Step by Step Solution

  1. Step 1: Write the proportion equation
    1,309.85 : 1,965.23 = 822.32 : x
  2. Step 2: Convert to fraction form
    1,309.85/1,965.23 = 822.32/x
  3. Step 3: Cross multiply
    1,309.85x = 1,965.23 × 822.32
  4. Step 4: Simplify right side
    1,309.85x = 1,616,034.00
  5. Step 5: Solve for x
    x = 1,616,034.00/1,309.85
  6. Step 6: Final answer
    x = 1,233.76

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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.