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Finding the Third Proportional to 977 and 2,069

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Solution

The third proportional to 977 and 2,069 is: 4,381.54

Step by Step Solution

  1. Step 1: Write the proportion equation
    977 : 2,069 = 2,069 : x
  2. Step 2: Convert to fraction form
    977/2,069 = 2,069/x
  3. Step 3: Cross multiply
    977x = 2,069 × 2,069
  4. Step 4: Simplify right side
    977x = 4,280,761
  5. Step 5: Solve for x
    x = 4,280,761/977
  6. Step 6: Final answer
    x = 4,381.54

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Why These Related Problems?

These problems maintain the same ratio (2.12) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.