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Finding the Third Proportional to 7,677 and 16,417

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Solution

The third proportional to 7,677 and 16,417 is: 35,107.19

Step by Step Solution

  1. Step 1: Write the proportion equation
    7,677 : 16,417 = 16,417 : x
  2. Step 2: Convert to fraction form
    7,677/16,417 = 16,417/x
  3. Step 3: Cross multiply
    7,677x = 16,417 × 16,417
  4. Step 4: Simplify right side
    7,677x = 269,517,889
  5. Step 5: Solve for x
    x = 269,517,889/7,677
  6. Step 6: Final answer
    x = 35,107.19

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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.