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Finding the Third Proportional to 5,965 and 13,097

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Solution

The third proportional to 5,965 and 13,097 is: 28,756.31

Step by Step Solution

  1. Step 1: Write the proportion equation
    5,965 : 13,097 = 13,097 : x
  2. Step 2: Convert to fraction form
    5,965/13,097 = 13,097/x
  3. Step 3: Cross multiply
    5,965x = 13,097 × 13,097
  4. Step 4: Simplify right side
    5,965x = 171,531,409
  5. Step 5: Solve for x
    x = 171,531,409/5,965
  6. Step 6: Final answer
    x = 28,756.31

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Why These Related Problems?

These problems maintain the same ratio (2.20) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.