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Finding the Third Proportional to 1,681 and 2,609

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Solution

The third proportional to 1,681 and 2,609 is: 4,049.30

Step by Step Solution

  1. Step 1: Write the proportion equation
    1,681 : 2,609 = 2,609 : x
  2. Step 2: Convert to fraction form
    1,681/2,609 = 2,609/x
  3. Step 3: Cross multiply
    1,681x = 2,609 × 2,609
  4. Step 4: Simplify right side
    1,681x = 6,806,881
  5. Step 5: Solve for x
    x = 6,806,881/1,681
  6. Step 6: Final answer
    x = 4,049.30

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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.