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Finding the Third Proportional to 9,744 and 20,178

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Solution

The third proportional to 9,744 and 20,178 is: 41,784.86

Step by Step Solution

  1. Step 1: Write the proportion equation
    9,744 : 20,178 = 20,178 : x
  2. Step 2: Convert to fraction form
    9,744/20,178 = 20,178/x
  3. Step 3: Cross multiply
    9,744x = 20,178 × 20,178
  4. Step 4: Simplify right side
    9,744x = 407,151,684
  5. Step 5: Solve for x
    x = 407,151,684/9,744
  6. Step 6: Final answer
    x = 41,784.86

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Why These Related Problems?

These problems maintain the same ratio (2.07) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.