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Finding the Third Proportional to 5,738 and 7,742

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Solution

The third proportional to 5,738 and 7,742 is: 10,445.90

Step by Step Solution

  1. Step 1: Write the proportion equation
    5,738 : 7,742 = 7,742 : x
  2. Step 2: Convert to fraction form
    5,738/7,742 = 7,742/x
  3. Step 3: Cross multiply
    5,738x = 7,742 × 7,742
  4. Step 4: Simplify right side
    5,738x = 59,938,564
  5. Step 5: Solve for x
    x = 59,938,564/5,738
  6. Step 6: Final answer
    x = 10,445.90

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Why These Related Problems?

These problems maintain the same ratio (1.35) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.