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Finding the Third Proportional to 8,214 and 17,580

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Solution

The third proportional to 8,214 and 17,580 is: 37,625.57

Step by Step Solution

  1. Step 1: Write the proportion equation
    8,214 : 17,580 = 17,580 : x
  2. Step 2: Convert to fraction form
    8,214/17,580 = 17,580/x
  3. Step 3: Cross multiply
    8,214x = 17,580 × 17,580
  4. Step 4: Simplify right side
    8,214x = 309,056,400
  5. Step 5: Solve for x
    x = 309,056,400/8,214
  6. Step 6: Final answer
    x = 37,625.57

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Why These Related Problems?

These problems maintain the same ratio (2.14) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.