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Finding the Third Proportional to 13 and 19.78

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Solution

The third proportional to 13 and 19.78 is: 30.10

Step by Step Solution

  1. Step 1: Write the proportion equation
    13 : 19.78 = 19.78 : x
  2. Step 2: Convert to fraction form
    13/19.78 = 19.78/x
  3. Step 3: Cross multiply
    13x = 19.78 × 19.78
  4. Step 4: Simplify right side
    13x = 391.30
  5. Step 5: Solve for x
    x = 391.30/13
  6. Step 6: Final answer
    x = 30.10

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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.