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Finding the Third Proportional to 19,782 and 30,807

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Solution

The third proportional to 19,782 and 30,807 is: 47,976.51

Step by Step Solution

  1. Step 1: Write the proportion equation
    19,782 : 30,807 = 30,807 : x
  2. Step 2: Convert to fraction form
    19,782/30,807 = 30,807/x
  3. Step 3: Cross multiply
    19,782x = 30,807 × 30,807
  4. Step 4: Simplify right side
    19,782x = 949,071,249
  5. Step 5: Solve for x
    x = 949,071,249/19,782
  6. Step 6: Final answer
    x = 47,976.51

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Why These Related Problems?

These problems maintain the same ratio (1.56) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.