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Finding the Third Proportional to 657 and 1,403

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Solution

The third proportional to 657 and 1,403 is: 2,996.06

Step by Step Solution

  1. Step 1: Write the proportion equation
    657 : 1,403 = 1,403 : x
  2. Step 2: Convert to fraction form
    657/1,403 = 1,403/x
  3. Step 3: Cross multiply
    657x = 1,403 × 1,403
  4. Step 4: Simplify right side
    657x = 1,968,409
  5. Step 5: Solve for x
    x = 1,968,409/657
  6. Step 6: Final answer
    x = 2,996.06

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Why These Related Problems?

These problems maintain the same ratio (2.14) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.