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Finding the Third Proportional to 1,024 and 1,421

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Solution

The third proportional to 1,024 and 1,421 is: 1,971.92

Step by Step Solution

  1. Step 1: Write the proportion equation
    1,024 : 1,421 = 1,421 : x
  2. Step 2: Convert to fraction form
    1,024/1,421 = 1,421/x
  3. Step 3: Cross multiply
    1,024x = 1,421 × 1,421
  4. Step 4: Simplify right side
    1,024x = 2,019,241
  5. Step 5: Solve for x
    x = 2,019,241/1,024
  6. Step 6: Final answer
    x = 1,971.92

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Why These Related Problems?

These problems maintain the same ratio (1.39) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.