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Finding the Third Proportional to 5,142 and 7,701

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Solution

The third proportional to 5,142 and 7,701 is: 11,533.53

Step by Step Solution

  1. Step 1: Write the proportion equation
    5,142 : 7,701 = 7,701 : x
  2. Step 2: Convert to fraction form
    5,142/7,701 = 7,701/x
  3. Step 3: Cross multiply
    5,142x = 7,701 × 7,701
  4. Step 4: Simplify right side
    5,142x = 59,305,401
  5. Step 5: Solve for x
    x = 59,305,401/5,142
  6. Step 6: Final answer
    x = 11,533.53

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Why These Related Problems?

These problems maintain the same ratio (1.50) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.