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Finding the Third Proportional to 8,140 and 17,684

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Solution

The third proportional to 8,140 and 17,684 is: 38,418.16

Step by Step Solution

  1. Step 1: Write the proportion equation
    8,140 : 17,684 = 17,684 : x
  2. Step 2: Convert to fraction form
    8,140/17,684 = 17,684/x
  3. Step 3: Cross multiply
    8,140x = 17,684 × 17,684
  4. Step 4: Simplify right side
    8,140x = 312,723,856
  5. Step 5: Solve for x
    x = 312,723,856/8,140
  6. Step 6: Final answer
    x = 38,418.16

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Why These Related Problems?

These problems maintain the same ratio (2.17) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.