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Finding the Third Proportional to 5,198 and 7,509

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Solution

The third proportional to 5,198 and 7,509 is: 10,847.46

Step by Step Solution

  1. Step 1: Write the proportion equation
    5,198 : 7,509 = 7,509 : x
  2. Step 2: Convert to fraction form
    5,198/7,509 = 7,509/x
  3. Step 3: Cross multiply
    5,198x = 7,509 × 7,509
  4. Step 4: Simplify right side
    5,198x = 56,385,081
  5. Step 5: Solve for x
    x = 56,385,081/5,198
  6. Step 6: Final answer
    x = 10,847.46

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Why These Related Problems?

These problems maintain the same ratio (1.44) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.