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Finding the Third Proportional to 5,214 and 5,970

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Solution

The third proportional to 5,214 and 5,970 is: 6,835.62

Step by Step Solution

  1. Step 1: Write the proportion equation
    5,214 : 5,970 = 5,970 : x
  2. Step 2: Convert to fraction form
    5,214/5,970 = 5,970/x
  3. Step 3: Cross multiply
    5,214x = 5,970 × 5,970
  4. Step 4: Simplify right side
    5,214x = 35,640,900
  5. Step 5: Solve for x
    x = 35,640,900/5,214
  6. Step 6: Final answer
    x = 6,835.62

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Why These Related Problems?

These problems maintain the same ratio (1.14) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.