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Finding the Fourth Proportional to 209.42, 314.32 and 106.77

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Solution

The fourth proportional to 209.42, 314.32 and 106.77 is: 160.25

Step by Step Solution

  1. Step 1: Write the proportion equation
    209.42 : 314.32 = 106.77 : x
  2. Step 2: Convert to fraction form
    209.42/314.32 = 106.77/x
  3. Step 3: Cross multiply
    209.42x = 314.32 × 106.77
  4. Step 4: Simplify right side
    209.42x = 33,559.68
  5. Step 5: Solve for x
    x = 33,559.68/209.42
  6. Step 6: Final answer
    x = 160.25

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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.