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Finding the Third Proportional to 823 and 1,019

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Solution

The third proportional to 823 and 1,019 is: 1,261.68

Step by Step Solution

  1. Step 1: Write the proportion equation
    823 : 1,019 = 1,019 : x
  2. Step 2: Convert to fraction form
    823/1,019 = 1,019/x
  3. Step 3: Cross multiply
    823x = 1,019 × 1,019
  4. Step 4: Simplify right side
    823x = 1,038,361
  5. Step 5: Solve for x
    x = 1,038,361/823
  6. Step 6: Final answer
    x = 1,261.68

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Why These Related Problems?

These problems maintain the same ratio (1.24) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.