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Finding the Third Proportional to 6,214 and 7,302

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Solution

The third proportional to 6,214 and 7,302 is: 8,580.50

Step by Step Solution

  1. Step 1: Write the proportion equation
    6,214 : 7,302 = 7,302 : x
  2. Step 2: Convert to fraction form
    6,214/7,302 = 7,302/x
  3. Step 3: Cross multiply
    6,214x = 7,302 × 7,302
  4. Step 4: Simplify right side
    6,214x = 53,319,204
  5. Step 5: Solve for x
    x = 53,319,204/6,214
  6. Step 6: Final answer
    x = 8,580.50

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Why These Related Problems?

These problems maintain the same ratio (1.18) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.