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Finding the Third Proportional to 5,170 and 5,706

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Solution

The third proportional to 5,170 and 5,706 is: 6,297.57

Step by Step Solution

  1. Step 1: Write the proportion equation
    5,170 : 5,706 = 5,706 : x
  2. Step 2: Convert to fraction form
    5,170/5,706 = 5,706/x
  3. Step 3: Cross multiply
    5,170x = 5,706 × 5,706
  4. Step 4: Simplify right side
    5,170x = 32,558,436
  5. Step 5: Solve for x
    x = 32,558,436/5,170
  6. Step 6: Final answer
    x = 6,297.57

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Why These Related Problems?

These problems maintain the same ratio (1.10) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.