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Finding the Third Proportional to 9,585 and 14,013

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Solution

The third proportional to 9,585 and 14,013 is: 20,486.61

Step by Step Solution

  1. Step 1: Write the proportion equation
    9,585 : 14,013 = 14,013 : x
  2. Step 2: Convert to fraction form
    9,585/14,013 = 14,013/x
  3. Step 3: Cross multiply
    9,585x = 14,013 × 14,013
  4. Step 4: Simplify right side
    9,585x = 196,364,169
  5. Step 5: Solve for x
    x = 196,364,169/9,585
  6. Step 6: Final answer
    x = 20,486.61

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Why These Related Problems?

These problems maintain the same ratio (1.46) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.