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Finding the Third Proportional to 1,082 and 1,407

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Solution

The third proportional to 1,082 and 1,407 is: 1,829.62

Step by Step Solution

  1. Step 1: Write the proportion equation
    1,082 : 1,407 = 1,407 : x
  2. Step 2: Convert to fraction form
    1,082/1,407 = 1,407/x
  3. Step 3: Cross multiply
    1,082x = 1,407 × 1,407
  4. Step 4: Simplify right side
    1,082x = 1,979,649
  5. Step 5: Solve for x
    x = 1,979,649/1,082
  6. Step 6: Final answer
    x = 1,829.62

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Why These Related Problems?

These problems maintain the same ratio (1.30) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.