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Finding the Third Proportional to 523 and 1,247

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Solution

The third proportional to 523 and 1,247 is: 2,973.25

Step by Step Solution

  1. Step 1: Write the proportion equation
    523 : 1,247 = 1,247 : x
  2. Step 2: Convert to fraction form
    523/1,247 = 1,247/x
  3. Step 3: Cross multiply
    523x = 1,247 × 1,247
  4. Step 4: Simplify right side
    523x = 1,555,009
  5. Step 5: Solve for x
    x = 1,555,009/523
  6. Step 6: Final answer
    x = 2,973.25

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Why These Related Problems?

These problems maintain the same ratio (2.38) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.