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Finding the Fourth Proportional to 1,223.64, 1,686.06 and 829.98

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Solution

The fourth proportional to 1,223.64, 1,686.06 and 829.98 is: 1,143.63

Step by Step Solution

  1. Step 1: Write the proportion equation
    1,223.64 : 1,686.06 = 829.98 : x
  2. Step 2: Convert to fraction form
    1,223.64/1,686.06 = 829.98/x
  3. Step 3: Cross multiply
    1,223.64x = 1,686.06 × 829.98
  4. Step 4: Simplify right side
    1,223.64x = 1,399,396.08
  5. Step 5: Solve for x
    x = 1,399,396.08/1,223.64
  6. Step 6: Final answer
    x = 1,143.63

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Why These Related Problems?

These problems maintain the same ratio (1.38) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.