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Finding the Third Proportional to 7,825 and 17,102

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Solution

The third proportional to 7,825 and 17,102 is: 37,377.43

Step by Step Solution

  1. Step 1: Write the proportion equation
    7,825 : 17,102 = 17,102 : x
  2. Step 2: Convert to fraction form
    7,825/17,102 = 17,102/x
  3. Step 3: Cross multiply
    7,825x = 17,102 × 17,102
  4. Step 4: Simplify right side
    7,825x = 292,478,404
  5. Step 5: Solve for x
    x = 292,478,404/7,825
  6. Step 6: Final answer
    x = 37,377.43

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Why These Related Problems?

These problems maintain the same ratio (2.19) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.