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Finding the Fourth Proportional to 109.77, 164.84 and 82.35

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Solution

The fourth proportional to 109.77, 164.84 and 82.35 is: 123.66

Step by Step Solution

  1. Step 1: Write the proportion equation
    109.77 : 164.84 = 82.35 : x
  2. Step 2: Convert to fraction form
    109.77/164.84 = 82.35/x
  3. Step 3: Cross multiply
    109.77x = 164.84 × 82.35
  4. Step 4: Simplify right side
    109.77x = 13,574.57
  5. Step 5: Solve for x
    x = 13,574.57/109.77
  6. Step 6: Final answer
    x = 123.66

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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.