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Finding the Third Proportional to 7,732 and 10,214

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Solution

The third proportional to 7,732 and 10,214 is: 13,492.73

Step by Step Solution

  1. Step 1: Write the proportion equation
    7,732 : 10,214 = 10,214 : x
  2. Step 2: Convert to fraction form
    7,732/10,214 = 10,214/x
  3. Step 3: Cross multiply
    7,732x = 10,214 × 10,214
  4. Step 4: Simplify right side
    7,732x = 104,325,796
  5. Step 5: Solve for x
    x = 104,325,796/7,732
  6. Step 6: Final answer
    x = 13,492.73

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Why These Related Problems?

These problems maintain the same ratio (1.32) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.