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Finding the Third Proportional to 5,790 and 13,538

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Solution

The third proportional to 5,790 and 13,538 is: 31,654.14

Step by Step Solution

  1. Step 1: Write the proportion equation
    5,790 : 13,538 = 13,538 : x
  2. Step 2: Convert to fraction form
    5,790/13,538 = 13,538/x
  3. Step 3: Cross multiply
    5,790x = 13,538 × 13,538
  4. Step 4: Simplify right side
    5,790x = 183,277,444
  5. Step 5: Solve for x
    x = 183,277,444/5,790
  6. Step 6: Final answer
    x = 31,654.14

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Why These Related Problems?

These problems maintain the same ratio (2.34) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.