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Finding the Third Proportional to 1,463 and 3,209

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Solution

The third proportional to 1,463 and 3,209 is: 7,038.74

Step by Step Solution

  1. Step 1: Write the proportion equation
    1,463 : 3,209 = 3,209 : x
  2. Step 2: Convert to fraction form
    1,463/3,209 = 3,209/x
  3. Step 3: Cross multiply
    1,463x = 3,209 × 3,209
  4. Step 4: Simplify right side
    1,463x = 10,297,681
  5. Step 5: Solve for x
    x = 10,297,681/1,463
  6. Step 6: Final answer
    x = 7,038.74

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Why These Related Problems?

These problems maintain the same ratio (2.19) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.