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Finding the Third Proportional to 469 and 1,012

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Solution

The third proportional to 469 and 1,012 is: 2,183.68

Step by Step Solution

  1. Step 1: Write the proportion equation
    469 : 1,012 = 1,012 : x
  2. Step 2: Convert to fraction form
    469/1,012 = 1,012/x
  3. Step 3: Cross multiply
    469x = 1,012 × 1,012
  4. Step 4: Simplify right side
    469x = 1,024,144
  5. Step 5: Solve for x
    x = 1,024,144/469
  6. Step 6: Final answer
    x = 2,183.68

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Why These Related Problems?

These problems maintain the same ratio (2.16) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.