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Finding the Third Proportional to 7,564 and 10,226

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Solution

The third proportional to 7,564 and 10,226 is: 13,824.84

Step by Step Solution

  1. Step 1: Write the proportion equation
    7,564 : 10,226 = 10,226 : x
  2. Step 2: Convert to fraction form
    7,564/10,226 = 10,226/x
  3. Step 3: Cross multiply
    7,564x = 10,226 × 10,226
  4. Step 4: Simplify right side
    7,564x = 104,571,076
  5. Step 5: Solve for x
    x = 104,571,076/7,564
  6. Step 6: Final answer
    x = 13,824.84

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Why These Related Problems?

These problems maintain the same ratio (1.35) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.