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Finding the Fourth Proportional to 206.40, 309.42 and 78.24

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Solution

The fourth proportional to 206.40, 309.42 and 78.24 is: 117.29

Step by Step Solution

  1. Step 1: Write the proportion equation
    206.40 : 309.42 = 78.24 : x
  2. Step 2: Convert to fraction form
    206.40/309.42 = 78.24/x
  3. Step 3: Cross multiply
    206.40x = 309.42 × 78.24
  4. Step 4: Simplify right side
    206.40x = 24,209.79
  5. Step 5: Solve for x
    x = 24,209.79/206.40
  6. Step 6: Final answer
    x = 117.29

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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.