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Finding the Third Proportional to 8,194 and 19,257

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Solution

The third proportional to 8,194 and 19,257 is: 45,256.54

Step by Step Solution

  1. Step 1: Write the proportion equation
    8,194 : 19,257 = 19,257 : x
  2. Step 2: Convert to fraction form
    8,194/19,257 = 19,257/x
  3. Step 3: Cross multiply
    8,194x = 19,257 × 19,257
  4. Step 4: Simplify right side
    8,194x = 370,832,049
  5. Step 5: Solve for x
    x = 370,832,049/8,194
  6. Step 6: Final answer
    x = 45,256.54

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Why These Related Problems?

These problems maintain the same ratio (2.35) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.