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Finding the Third Proportional to 825 and 1,257

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Solution

The third proportional to 825 and 1,257 is: 1,915.21

Step by Step Solution

  1. Step 1: Write the proportion equation
    825 : 1,257 = 1,257 : x
  2. Step 2: Convert to fraction form
    825/1,257 = 1,257/x
  3. Step 3: Cross multiply
    825x = 1,257 × 1,257
  4. Step 4: Simplify right side
    825x = 1,580,049
  5. Step 5: Solve for x
    x = 1,580,049/825
  6. Step 6: Final answer
    x = 1,915.21

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Why These Related Problems?

These problems maintain the same ratio (1.52) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.