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Finding the Third Proportional to 3,209 and 4,814

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Solution

The third proportional to 3,209 and 4,814 is: 7,221.75

Step by Step Solution

  1. Step 1: Write the proportion equation
    3,209 : 4,814 = 4,814 : x
  2. Step 2: Convert to fraction form
    3,209/4,814 = 4,814/x
  3. Step 3: Cross multiply
    3,209x = 4,814 × 4,814
  4. Step 4: Simplify right side
    3,209x = 23,174,596
  5. Step 5: Solve for x
    x = 23,174,596/3,209
  6. Step 6: Final answer
    x = 7,221.75

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Why These Related Problems?

These problems maintain the same ratio (1.50) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.