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Finding the Third Proportional to 1,537 and 2,086

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Solution

The third proportional to 1,537 and 2,086 is: 2,831.10

Step by Step Solution

  1. Step 1: Write the proportion equation
    1,537 : 2,086 = 2,086 : x
  2. Step 2: Convert to fraction form
    1,537/2,086 = 2,086/x
  3. Step 3: Cross multiply
    1,537x = 2,086 × 2,086
  4. Step 4: Simplify right side
    1,537x = 4,351,396
  5. Step 5: Solve for x
    x = 4,351,396/1,537
  6. Step 6: Final answer
    x = 2,831.10

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Why These Related Problems?

These problems maintain the same ratio (1.36) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.