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Finding the Third Proportional to 5,780 and 13,486

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Solution

The third proportional to 5,780 and 13,486 is: 31,465.78

Step by Step Solution

  1. Step 1: Write the proportion equation
    5,780 : 13,486 = 13,486 : x
  2. Step 2: Convert to fraction form
    5,780/13,486 = 13,486/x
  3. Step 3: Cross multiply
    5,780x = 13,486 × 13,486
  4. Step 4: Simplify right side
    5,780x = 181,872,196
  5. Step 5: Solve for x
    x = 181,872,196/5,780
  6. Step 6: Final answer
    x = 31,465.78

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Why These Related Problems?

These problems maintain the same ratio (2.33) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.