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Finding the Third Proportional to 500 and 1,012

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Solution

The third proportional to 500 and 1,012 is: 2,048.29

Step by Step Solution

  1. Step 1: Write the proportion equation
    500 : 1,012 = 1,012 : x
  2. Step 2: Convert to fraction form
    500/1,012 = 1,012/x
  3. Step 3: Cross multiply
    500x = 1,012 × 1,012
  4. Step 4: Simplify right side
    500x = 1,024,144
  5. Step 5: Solve for x
    x = 1,024,144/500
  6. Step 6: Final answer
    x = 2,048.29

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Why These Related Problems?

These problems maintain the same ratio (2.02) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.