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Finding the Third Proportional to 5,852 and 8,230

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Solution

The third proportional to 5,852 and 8,230 is: 11,574.32

Step by Step Solution

  1. Step 1: Write the proportion equation
    5,852 : 8,230 = 8,230 : x
  2. Step 2: Convert to fraction form
    5,852/8,230 = 8,230/x
  3. Step 3: Cross multiply
    5,852x = 8,230 × 8,230
  4. Step 4: Simplify right side
    5,852x = 67,732,900
  5. Step 5: Solve for x
    x = 67,732,900/5,852
  6. Step 6: Final answer
    x = 11,574.32

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Why These Related Problems?

These problems maintain the same ratio (1.41) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.