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Finding the Third Proportional to 4,196 and 6,503

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Solution

The third proportional to 4,196 and 6,503 is: 10,078.41

Step by Step Solution

  1. Step 1: Write the proportion equation
    4,196 : 6,503 = 6,503 : x
  2. Step 2: Convert to fraction form
    4,196/6,503 = 6,503/x
  3. Step 3: Cross multiply
    4,196x = 6,503 × 6,503
  4. Step 4: Simplify right side
    4,196x = 42,289,009
  5. Step 5: Solve for x
    x = 42,289,009/4,196
  6. Step 6: Final answer
    x = 10,078.41

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Why These Related Problems?

These problems maintain the same ratio (1.55) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.