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Finding the Third Proportional to 1,407 and 3,657

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Solution

The third proportional to 1,407 and 3,657 is: 9,505.08

Step by Step Solution

  1. Step 1: Write the proportion equation
    1,407 : 3,657 = 3,657 : x
  2. Step 2: Convert to fraction form
    1,407/3,657 = 3,657/x
  3. Step 3: Cross multiply
    1,407x = 3,657 × 3,657
  4. Step 4: Simplify right side
    1,407x = 13,373,649
  5. Step 5: Solve for x
    x = 13,373,649/1,407
  6. Step 6: Final answer
    x = 9,505.08

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These problems maintain the same ratio (2.60) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.