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Finding the Third Proportional to 13,205 and 19,741

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Solution

The third proportional to 13,205 and 19,741 is: 29,512.08

Step by Step Solution

  1. Step 1: Write the proportion equation
    13,205 : 19,741 = 19,741 : x
  2. Step 2: Convert to fraction form
    13,205/19,741 = 19,741/x
  3. Step 3: Cross multiply
    13,205x = 19,741 × 19,741
  4. Step 4: Simplify right side
    13,205x = 389,707,081
  5. Step 5: Solve for x
    x = 389,707,081/13,205
  6. Step 6: Final answer
    x = 29,512.08

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Why These Related Problems?

These problems maintain the same ratio (1.49) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.