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Finding the Third Proportional to 830 and 1,422

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Solution

The third proportional to 830 and 1,422 is: 2,436.25

Step by Step Solution

  1. Step 1: Write the proportion equation
    830 : 1,422 = 1,422 : x
  2. Step 2: Convert to fraction form
    830/1,422 = 1,422/x
  3. Step 3: Cross multiply
    830x = 1,422 × 1,422
  4. Step 4: Simplify right side
    830x = 2,022,084
  5. Step 5: Solve for x
    x = 2,022,084/830
  6. Step 6: Final answer
    x = 2,436.25

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Why These Related Problems?

These problems maintain the same ratio (1.71) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.