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Finding the Third Proportional to 5,869 and 7,540

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Solution

The third proportional to 5,869 and 7,540 is: 9,686.76

Step by Step Solution

  1. Step 1: Write the proportion equation
    5,869 : 7,540 = 7,540 : x
  2. Step 2: Convert to fraction form
    5,869/7,540 = 7,540/x
  3. Step 3: Cross multiply
    5,869x = 7,540 × 7,540
  4. Step 4: Simplify right side
    5,869x = 56,851,600
  5. Step 5: Solve for x
    x = 56,851,600/5,869
  6. Step 6: Final answer
    x = 9,686.76

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Why These Related Problems?

These problems maintain the same ratio (1.28) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.