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Finding the Third Proportional to 5,742 and 7,748

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Solution

The third proportional to 5,742 and 7,748 is: 10,454.81

Step by Step Solution

  1. Step 1: Write the proportion equation
    5,742 : 7,748 = 7,748 : x
  2. Step 2: Convert to fraction form
    5,742/7,748 = 7,748/x
  3. Step 3: Cross multiply
    5,742x = 7,748 × 7,748
  4. Step 4: Simplify right side
    5,742x = 60,031,504
  5. Step 5: Solve for x
    x = 60,031,504/5,742
  6. Step 6: Final answer
    x = 10,454.81

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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.