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Finding the Third Proportional to 12,784 and 19,642

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Solution

The third proportional to 12,784 and 19,642 is: 30,178.99

Step by Step Solution

  1. Step 1: Write the proportion equation
    12,784 : 19,642 = 19,642 : x
  2. Step 2: Convert to fraction form
    12,784/19,642 = 19,642/x
  3. Step 3: Cross multiply
    12,784x = 19,642 × 19,642
  4. Step 4: Simplify right side
    12,784x = 385,808,164
  5. Step 5: Solve for x
    x = 385,808,164/12,784
  6. Step 6: Final answer
    x = 30,178.99

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Why These Related Problems?

These problems maintain the same ratio (1.54) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.