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Finding the Third Proportional to 31,106 and 47,814

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Solution

The third proportional to 31,106 and 47,814 is: 73,496.39

Step by Step Solution

  1. Step 1: Write the proportion equation
    31,106 : 47,814 = 47,814 : x
  2. Step 2: Convert to fraction form
    31,106/47,814 = 47,814/x
  3. Step 3: Cross multiply
    31,106x = 47,814 × 47,814
  4. Step 4: Simplify right side
    31,106x = 2,286,178,596
  5. Step 5: Solve for x
    x = 2,286,178,596/31,106
  6. Step 6: Final answer
    x = 73,496.39

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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.