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Finding the Third Proportional to 5,214 and 8,013

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Solution

The third proportional to 5,214 and 8,013 is: 12,314.57

Step by Step Solution

  1. Step 1: Write the proportion equation
    5,214 : 8,013 = 8,013 : x
  2. Step 2: Convert to fraction form
    5,214/8,013 = 8,013/x
  3. Step 3: Cross multiply
    5,214x = 8,013 × 8,013
  4. Step 4: Simplify right side
    5,214x = 64,208,169
  5. Step 5: Solve for x
    x = 64,208,169/5,214
  6. Step 6: Final answer
    x = 12,314.57

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Why These Related Problems?

These problems maintain the same ratio (1.54) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.