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Finding the Third Proportional to 7,746 and 8,370

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Solution

The third proportional to 7,746 and 8,370 is: 9,044.27

Step by Step Solution

  1. Step 1: Write the proportion equation
    7,746 : 8,370 = 8,370 : x
  2. Step 2: Convert to fraction form
    7,746/8,370 = 8,370/x
  3. Step 3: Cross multiply
    7,746x = 8,370 × 8,370
  4. Step 4: Simplify right side
    7,746x = 70,056,900
  5. Step 5: Solve for x
    x = 70,056,900/7,746
  6. Step 6: Final answer
    x = 9,044.27

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Why These Related Problems?

These problems maintain the same ratio (1.08) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.