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Finding the Third Proportional to 105,238 and 157,977

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Solution

The third proportional to 105,238 and 157,977 is: 237,145.64

Step by Step Solution

  1. Step 1: Write the proportion equation
    105,238 : 157,977 = 157,977 : x
  2. Step 2: Convert to fraction form
    105,238/157,977 = 157,977/x
  3. Step 3: Cross multiply
    105,238x = 157,977 × 157,977
  4. Step 4: Simplify right side
    105,238x = 24,956,732,529
  5. Step 5: Solve for x
    x = 24,956,732,529/105,238
  6. Step 6: Final answer
    x = 237,145.64

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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.