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Finding the Third Proportional to 2,069 and 3,200

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Solution

The third proportional to 2,069 and 3,200 is: 4,949.25

Step by Step Solution

  1. Step 1: Write the proportion equation
    2,069 : 3,200 = 3,200 : x
  2. Step 2: Convert to fraction form
    2,069/3,200 = 3,200/x
  3. Step 3: Cross multiply
    2,069x = 3,200 × 3,200
  4. Step 4: Simplify right side
    2,069x = 10,240,000
  5. Step 5: Solve for x
    x = 10,240,000/2,069
  6. Step 6: Final answer
    x = 4,949.25

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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.