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Finding the Third Proportional to 825 and 1,003

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Solution

The third proportional to 825 and 1,003 is: 1,219.40

Step by Step Solution

  1. Step 1: Write the proportion equation
    825 : 1,003 = 1,003 : x
  2. Step 2: Convert to fraction form
    825/1,003 = 1,003/x
  3. Step 3: Cross multiply
    825x = 1,003 × 1,003
  4. Step 4: Simplify right side
    825x = 1,006,009
  5. Step 5: Solve for x
    x = 1,006,009/825
  6. Step 6: Final answer
    x = 1,219.40

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Why These Related Problems?

These problems maintain the same ratio (1.22) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.