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Finding the Third Proportional to 7,746 and 17,214

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Solution

The third proportional to 7,746 and 17,214 is: 38,254.81

Step by Step Solution

  1. Step 1: Write the proportion equation
    7,746 : 17,214 = 17,214 : x
  2. Step 2: Convert to fraction form
    7,746/17,214 = 17,214/x
  3. Step 3: Cross multiply
    7,746x = 17,214 × 17,214
  4. Step 4: Simplify right side
    7,746x = 296,321,796
  5. Step 5: Solve for x
    x = 296,321,796/7,746
  6. Step 6: Final answer
    x = 38,254.81

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Why These Related Problems?

These problems maintain the same ratio (2.22) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.