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Finding the Third Proportional to 12,816 and 19,534

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Solution

The third proportional to 12,816 and 19,534 is: 29,773.50

Step by Step Solution

  1. Step 1: Write the proportion equation
    12,816 : 19,534 = 19,534 : x
  2. Step 2: Convert to fraction form
    12,816/19,534 = 19,534/x
  3. Step 3: Cross multiply
    12,816x = 19,534 × 19,534
  4. Step 4: Simplify right side
    12,816x = 381,577,156
  5. Step 5: Solve for x
    x = 381,577,156/12,816
  6. Step 6: Final answer
    x = 29,773.50

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Why These Related Problems?

These problems maintain the same ratio (1.52) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.