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Finding the Third Proportional to 7,742 and 15,896

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Solution

The third proportional to 7,742 and 15,896 is: 32,637.93

Step by Step Solution

  1. Step 1: Write the proportion equation
    7,742 : 15,896 = 15,896 : x
  2. Step 2: Convert to fraction form
    7,742/15,896 = 15,896/x
  3. Step 3: Cross multiply
    7,742x = 15,896 × 15,896
  4. Step 4: Simplify right side
    7,742x = 252,682,816
  5. Step 5: Solve for x
    x = 252,682,816/7,742
  6. Step 6: Final answer
    x = 32,637.93

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Why These Related Problems?

These problems maintain the same ratio (2.05) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.