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Finding the Third Proportional to 77.84 and 145.23

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Solution

The third proportional to 77.84 and 145.23 is: 270.98

Step by Step Solution

  1. Step 1: Write the proportion equation
    77.84 : 145.23 = 145.23 : x
  2. Step 2: Convert to fraction form
    77.84/145.23 = 145.23/x
  3. Step 3: Cross multiply
    77.84x = 145.23 × 145.23
  4. Step 4: Simplify right side
    77.84x = 21,091.89
  5. Step 5: Solve for x
    x = 21,091.89/77.84
  6. Step 6: Final answer
    x = 270.98

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Why These Related Problems?

These problems maintain the same ratio (1.87) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.