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Finding the Third Proportional to 7,677 and 15,846

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Solution

The third proportional to 7,677 and 15,846 is: 32,707.53

Step by Step Solution

  1. Step 1: Write the proportion equation
    7,677 : 15,846 = 15,846 : x
  2. Step 2: Convert to fraction form
    7,677/15,846 = 15,846/x
  3. Step 3: Cross multiply
    7,677x = 15,846 × 15,846
  4. Step 4: Simplify right side
    7,677x = 251,095,716
  5. Step 5: Solve for x
    x = 251,095,716/7,677
  6. Step 6: Final answer
    x = 32,707.53

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Why These Related Problems?

These problems maintain the same ratio (2.06) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.