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Finding the Third Proportional to 501.75 and 1,027.97

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Solution

The third proportional to 501.75 and 1,027.97 is: 2,106.07

Step by Step Solution

  1. Step 1: Write the proportion equation
    501.75 : 1,027.97 = 1,027.97 : x
  2. Step 2: Convert to fraction form
    501.75/1,027.97 = 1,027.97/x
  3. Step 3: Cross multiply
    501.75x = 1,027.97 × 1,027.97
  4. Step 4: Simplify right side
    501.75x = 1,056,719.75
  5. Step 5: Solve for x
    x = 1,056,719.75/501.75
  6. Step 6: Final answer
    x = 2,106.07

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Why These Related Problems?

These problems maintain the same ratio (2.05) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.