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Finding the Third Proportional to 1,022 and 1,206

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Solution

The third proportional to 1,022 and 1,206 is: 1,423.13

Step by Step Solution

  1. Step 1: Write the proportion equation
    1,022 : 1,206 = 1,206 : x
  2. Step 2: Convert to fraction form
    1,022/1,206 = 1,206/x
  3. Step 3: Cross multiply
    1,022x = 1,206 × 1,206
  4. Step 4: Simplify right side
    1,022x = 1,454,436
  5. Step 5: Solve for x
    x = 1,454,436/1,022
  6. Step 6: Final answer
    x = 1,423.13

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Why These Related Problems?

These problems maintain the same ratio (1.18) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.