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Finding the Third Proportional to 2,258 and 2,782

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Solution

The third proportional to 2,258 and 2,782 is: 3,427.60

Step by Step Solution

  1. Step 1: Write the proportion equation
    2,258 : 2,782 = 2,782 : x
  2. Step 2: Convert to fraction form
    2,258/2,782 = 2,782/x
  3. Step 3: Cross multiply
    2,258x = 2,782 × 2,782
  4. Step 4: Simplify right side
    2,258x = 7,739,524
  5. Step 5: Solve for x
    x = 7,739,524/2,258
  6. Step 6: Final answer
    x = 3,427.60

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Why These Related Problems?

These problems maintain the same ratio (1.23) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.