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Finding the Third Proportional to 971 and 2,031

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Solution

The third proportional to 971 and 2,031 is: 4,248.16

Step by Step Solution

  1. Step 1: Write the proportion equation
    971 : 2,031 = 2,031 : x
  2. Step 2: Convert to fraction form
    971/2,031 = 2,031/x
  3. Step 3: Cross multiply
    971x = 2,031 × 2,031
  4. Step 4: Simplify right side
    971x = 4,124,961
  5. Step 5: Solve for x
    x = 4,124,961/971
  6. Step 6: Final answer
    x = 4,248.16

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Why These Related Problems?

These problems maintain the same ratio (2.09) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.