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Finding the Fourth Proportional to 214.78, 322.14 and 77.80

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Solution

The fourth proportional to 214.78, 322.14 and 77.80 is: 116.68

Step by Step Solution

  1. Step 1: Write the proportion equation
    214.78 : 322.14 = 77.80 : x
  2. Step 2: Convert to fraction form
    214.78/322.14 = 77.80/x
  3. Step 3: Cross multiply
    214.78x = 322.14 × 77.80
  4. Step 4: Simplify right side
    214.78x = 25,061.69
  5. Step 5: Solve for x
    x = 25,061.69/214.78
  6. Step 6: Final answer
    x = 116.68

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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.