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Finding the Third Proportional to 77 and 157

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Solution

The third proportional to 77 and 157 is: 320.12

Step by Step Solution

  1. Step 1: Write the proportion equation
    77 : 157 = 157 : x
  2. Step 2: Convert to fraction form
    77/157 = 157/x
  3. Step 3: Cross multiply
    77x = 157 × 157
  4. Step 4: Simplify right side
    77x = 24,649
  5. Step 5: Solve for x
    x = 24,649/77
  6. Step 6: Final answer
    x = 320.12

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Why These Related Problems?

These problems maintain the same ratio (2.04) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.