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Finding the Fourth Proportional to 1,309.47, 1,965.51 and 823.74

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Solution

The fourth proportional to 1,309.47, 1,965.51 and 823.74 is: 1,236.43

Step by Step Solution

  1. Step 1: Write the proportion equation
    1,309.47 : 1,965.51 = 823.74 : x
  2. Step 2: Convert to fraction form
    1,309.47/1,965.51 = 823.74/x
  3. Step 3: Cross multiply
    1,309.47x = 1,965.51 × 823.74
  4. Step 4: Simplify right side
    1,309.47x = 1,619,069.21
  5. Step 5: Solve for x
    x = 1,619,069.21/1,309.47
  6. Step 6: Final answer
    x = 1,236.43

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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.