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Finding the Third Proportional to 1,407 and 1,665

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Solution

The third proportional to 1,407 and 1,665 is: 1,970.31

Step by Step Solution

  1. Step 1: Write the proportion equation
    1,407 : 1,665 = 1,665 : x
  2. Step 2: Convert to fraction form
    1,407/1,665 = 1,665/x
  3. Step 3: Cross multiply
    1,407x = 1,665 × 1,665
  4. Step 4: Simplify right side
    1,407x = 2,772,225
  5. Step 5: Solve for x
    x = 2,772,225/1,407
  6. Step 6: Final answer
    x = 1,970.31

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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.