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Finding the Third Proportional to 947 and 1,031

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Solution

The third proportional to 947 and 1,031 is: 1,122.45

Step by Step Solution

  1. Step 1: Write the proportion equation
    947 : 1,031 = 1,031 : x
  2. Step 2: Convert to fraction form
    947/1,031 = 1,031/x
  3. Step 3: Cross multiply
    947x = 1,031 × 1,031
  4. Step 4: Simplify right side
    947x = 1,062,961
  5. Step 5: Solve for x
    x = 1,062,961/947
  6. Step 6: Final answer
    x = 1,122.45

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Why These Related Problems?

These problems maintain the same ratio (1.09) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.