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Finding the Third Proportional to 12,840 and 20,534

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Solution

The third proportional to 12,840 and 20,534 is: 32,838.41

Step by Step Solution

  1. Step 1: Write the proportion equation
    12,840 : 20,534 = 20,534 : x
  2. Step 2: Convert to fraction form
    12,840/20,534 = 20,534/x
  3. Step 3: Cross multiply
    12,840x = 20,534 × 20,534
  4. Step 4: Simplify right side
    12,840x = 421,645,156
  5. Step 5: Solve for x
    x = 421,645,156/12,840
  6. Step 6: Final answer
    x = 32,838.41

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Why These Related Problems?

These problems maintain the same ratio (1.60) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.