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Finding the Third Proportional to 491 and 1,023

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Solution

The third proportional to 491 and 1,023 is: 2,131.42

Step by Step Solution

  1. Step 1: Write the proportion equation
    491 : 1,023 = 1,023 : x
  2. Step 2: Convert to fraction form
    491/1,023 = 1,023/x
  3. Step 3: Cross multiply
    491x = 1,023 × 1,023
  4. Step 4: Simplify right side
    491x = 1,046,529
  5. Step 5: Solve for x
    x = 1,046,529/491
  6. Step 6: Final answer
    x = 2,131.42

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Why These Related Problems?

These problems maintain the same ratio (2.08) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.