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Finding the Third Proportional to 997 and 1,535

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Solution

The third proportional to 997 and 1,535 is: 2,363.31

Step by Step Solution

  1. Step 1: Write the proportion equation
    997 : 1,535 = 1,535 : x
  2. Step 2: Convert to fraction form
    997/1,535 = 1,535/x
  3. Step 3: Cross multiply
    997x = 1,535 × 1,535
  4. Step 4: Simplify right side
    997x = 2,356,225
  5. Step 5: Solve for x
    x = 2,356,225/997
  6. Step 6: Final answer
    x = 2,363.31

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Why These Related Problems?

These problems maintain the same ratio (1.54) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.