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Finding the Third Proportional to 13,584 and 31,368

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Solution

The third proportional to 13,584 and 31,368 is: 72,434.59

Step by Step Solution

  1. Step 1: Write the proportion equation
    13,584 : 31,368 = 31,368 : x
  2. Step 2: Convert to fraction form
    13,584/31,368 = 31,368/x
  3. Step 3: Cross multiply
    13,584x = 31,368 × 31,368
  4. Step 4: Simplify right side
    13,584x = 983,951,424
  5. Step 5: Solve for x
    x = 983,951,424/13,584
  6. Step 6: Final answer
    x = 72,434.59

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Why These Related Problems?

These problems maintain the same ratio (2.31) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.