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Finding the Third Proportional to 4,091 and 5,971

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Solution

The third proportional to 4,091 and 5,971 is: 8,714.95

Step by Step Solution

  1. Step 1: Write the proportion equation
    4,091 : 5,971 = 5,971 : x
  2. Step 2: Convert to fraction form
    4,091/5,971 = 5,971/x
  3. Step 3: Cross multiply
    4,091x = 5,971 × 5,971
  4. Step 4: Simplify right side
    4,091x = 35,652,841
  5. Step 5: Solve for x
    x = 35,652,841/4,091
  6. Step 6: Final answer
    x = 8,714.95

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Why These Related Problems?

These problems maintain the same ratio (1.46) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.