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Finding the Third Proportional to 6,194 and 13,412

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Solution

The third proportional to 6,194 and 13,412 is: 29,041.29

Step by Step Solution

  1. Step 1: Write the proportion equation
    6,194 : 13,412 = 13,412 : x
  2. Step 2: Convert to fraction form
    6,194/13,412 = 13,412/x
  3. Step 3: Cross multiply
    6,194x = 13,412 × 13,412
  4. Step 4: Simplify right side
    6,194x = 179,881,744
  5. Step 5: Solve for x
    x = 179,881,744/6,194
  6. Step 6: Final answer
    x = 29,041.29

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Why These Related Problems?

These problems maintain the same ratio (2.17) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.