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Finding the Third Proportional to 2,056 and 2,742

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Solution

The third proportional to 2,056 and 2,742 is: 3,656.89

Step by Step Solution

  1. Step 1: Write the proportion equation
    2,056 : 2,742 = 2,742 : x
  2. Step 2: Convert to fraction form
    2,056/2,742 = 2,742/x
  3. Step 3: Cross multiply
    2,056x = 2,742 × 2,742
  4. Step 4: Simplify right side
    2,056x = 7,518,564
  5. Step 5: Solve for x
    x = 7,518,564/2,056
  6. Step 6: Final answer
    x = 3,656.89

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Why These Related Problems?

These problems maintain the same ratio (1.33) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.