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Finding the Third Proportional to 21,197 and 32,069

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Solution

The third proportional to 21,197 and 32,069 is: 48,517.28

Step by Step Solution

  1. Step 1: Write the proportion equation
    21,197 : 32,069 = 32,069 : x
  2. Step 2: Convert to fraction form
    21,197/32,069 = 32,069/x
  3. Step 3: Cross multiply
    21,197x = 32,069 × 32,069
  4. Step 4: Simplify right side
    21,197x = 1,028,420,761
  5. Step 5: Solve for x
    x = 1,028,420,761/21,197
  6. Step 6: Final answer
    x = 48,517.28

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Why These Related Problems?

These problems maintain the same ratio (1.51) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.