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Finding the Third Proportional to 12,194 and 19,259

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Solution

The third proportional to 12,194 and 19,259 is: 30,417.34

Step by Step Solution

  1. Step 1: Write the proportion equation
    12,194 : 19,259 = 19,259 : x
  2. Step 2: Convert to fraction form
    12,194/19,259 = 19,259/x
  3. Step 3: Cross multiply
    12,194x = 19,259 × 19,259
  4. Step 4: Simplify right side
    12,194x = 370,909,081
  5. Step 5: Solve for x
    x = 370,909,081/12,194
  6. Step 6: Final answer
    x = 30,417.34

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Why These Related Problems?

These problems maintain the same ratio (1.58) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.