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Finding the Third Proportional to 8,640 and 13,214

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Solution

The third proportional to 8,640 and 13,214 is: 20,209.47

Step by Step Solution

  1. Step 1: Write the proportion equation
    8,640 : 13,214 = 13,214 : x
  2. Step 2: Convert to fraction form
    8,640/13,214 = 13,214/x
  3. Step 3: Cross multiply
    8,640x = 13,214 × 13,214
  4. Step 4: Simplify right side
    8,640x = 174,609,796
  5. Step 5: Solve for x
    x = 174,609,796/8,640
  6. Step 6: Final answer
    x = 20,209.47

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Why These Related Problems?

These problems maintain the same ratio (1.53) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.