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Finding the Fourth Proportional to 109.77, 164.49 and 82.23

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Solution

The fourth proportional to 109.77, 164.49 and 82.23 is: 123.22

Step by Step Solution

  1. Step 1: Write the proportion equation
    109.77 : 164.49 = 82.23 : x
  2. Step 2: Convert to fraction form
    109.77/164.49 = 82.23/x
  3. Step 3: Cross multiply
    109.77x = 164.49 × 82.23
  4. Step 4: Simplify right side
    109.77x = 13,526.01
  5. Step 5: Solve for x
    x = 13,526.01/109.77
  6. Step 6: Final answer
    x = 123.22

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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.