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Finding the Third Proportional to 1,022 and 2,056

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Solution

The third proportional to 1,022 and 2,056 is: 4,136.14

Step by Step Solution

  1. Step 1: Write the proportion equation
    1,022 : 2,056 = 2,056 : x
  2. Step 2: Convert to fraction form
    1,022/2,056 = 2,056/x
  3. Step 3: Cross multiply
    1,022x = 2,056 × 2,056
  4. Step 4: Simplify right side
    1,022x = 4,227,136
  5. Step 5: Solve for x
    x = 4,227,136/1,022
  6. Step 6: Final answer
    x = 4,136.14

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Why These Related Problems?

These problems maintain the same ratio (2.01) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.