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Finding the Third Proportional to 51.84 and 77.77

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Solution

The third proportional to 51.84 and 77.77 is: 116.65

Step by Step Solution

  1. Step 1: Write the proportion equation
    51.84 : 77.77 = 77.77 : x
  2. Step 2: Convert to fraction form
    51.84/77.77 = 77.77/x
  3. Step 3: Cross multiply
    51.84x = 77.77 × 77.77
  4. Step 4: Simplify right side
    51.84x = 6,047.49
  5. Step 5: Solve for x
    x = 6,047.49/51.84
  6. Step 6: Final answer
    x = 116.65

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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.