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Finding the Third Proportional to 971 and 1,964

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Solution

The third proportional to 971 and 1,964 is: 3,972.50

Step by Step Solution

  1. Step 1: Write the proportion equation
    971 : 1,964 = 1,964 : x
  2. Step 2: Convert to fraction form
    971/1,964 = 1,964/x
  3. Step 3: Cross multiply
    971x = 1,964 × 1,964
  4. Step 4: Simplify right side
    971x = 3,857,296
  5. Step 5: Solve for x
    x = 3,857,296/971
  6. Step 6: Final answer
    x = 3,972.50

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Why These Related Problems?

These problems maintain the same ratio (2.02) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.