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Finding the Third Proportional to 8,420 and 9,164

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Solution

The third proportional to 8,420 and 9,164 is: 9,973.74

Step by Step Solution

  1. Step 1: Write the proportion equation
    8,420 : 9,164 = 9,164 : x
  2. Step 2: Convert to fraction form
    8,420/9,164 = 9,164/x
  3. Step 3: Cross multiply
    8,420x = 9,164 × 9,164
  4. Step 4: Simplify right side
    8,420x = 83,978,896
  5. Step 5: Solve for x
    x = 83,978,896/8,420
  6. Step 6: Final answer
    x = 9,973.74

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Why These Related Problems?

These problems maintain the same ratio (1.09) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.