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Finding the Third Proportional to 77 and 106.50

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Solution

The third proportional to 77 and 106.50 is: 147.30

Step by Step Solution

  1. Step 1: Write the proportion equation
    77 : 106.50 = 106.50 : x
  2. Step 2: Convert to fraction form
    77/106.50 = 106.50/x
  3. Step 3: Cross multiply
    77x = 106.50 × 106.50
  4. Step 4: Simplify right side
    77x = 11,342.25
  5. Step 5: Solve for x
    x = 11,342.25/77
  6. Step 6: Final answer
    x = 147.30

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Why These Related Problems?

These problems maintain the same ratio (1.38) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.