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Finding the Third Proportional to 1,537 and 2,062

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Solution

The third proportional to 1,537 and 2,062 is: 2,766.33

Step by Step Solution

  1. Step 1: Write the proportion equation
    1,537 : 2,062 = 2,062 : x
  2. Step 2: Convert to fraction form
    1,537/2,062 = 2,062/x
  3. Step 3: Cross multiply
    1,537x = 2,062 × 2,062
  4. Step 4: Simplify right side
    1,537x = 4,251,844
  5. Step 5: Solve for x
    x = 4,251,844/1,537
  6. Step 6: Final answer
    x = 2,766.33

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Why These Related Problems?

These problems maintain the same ratio (1.34) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.