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Finding the Third Proportional to 977 and 1,611

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Solution

The third proportional to 977 and 1,611 is: 2,656.42

Step by Step Solution

  1. Step 1: Write the proportion equation
    977 : 1,611 = 1,611 : x
  2. Step 2: Convert to fraction form
    977/1,611 = 1,611/x
  3. Step 3: Cross multiply
    977x = 1,611 × 1,611
  4. Step 4: Simplify right side
    977x = 2,595,321
  5. Step 5: Solve for x
    x = 2,595,321/977
  6. Step 6: Final answer
    x = 2,656.42

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Why These Related Problems?

These problems maintain the same ratio (1.65) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.