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Finding the Third Proportional to 8,340 and 9,564

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Solution

The third proportional to 8,340 and 9,564 is: 10,967.64

Step by Step Solution

  1. Step 1: Write the proportion equation
    8,340 : 9,564 = 9,564 : x
  2. Step 2: Convert to fraction form
    8,340/9,564 = 9,564/x
  3. Step 3: Cross multiply
    8,340x = 9,564 × 9,564
  4. Step 4: Simplify right side
    8,340x = 91,470,096
  5. Step 5: Solve for x
    x = 91,470,096/8,340
  6. Step 6: Final answer
    x = 10,967.64

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Why These Related Problems?

These problems maintain the same ratio (1.15) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.