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Finding the Third Proportional to 1,029 and 1,065

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Solution

The third proportional to 1,029 and 1,065 is: 1,102.26

Step by Step Solution

  1. Step 1: Write the proportion equation
    1,029 : 1,065 = 1,065 : x
  2. Step 2: Convert to fraction form
    1,029/1,065 = 1,065/x
  3. Step 3: Cross multiply
    1,029x = 1,065 × 1,065
  4. Step 4: Simplify right side
    1,029x = 1,134,225
  5. Step 5: Solve for x
    x = 1,134,225/1,029
  6. Step 6: Final answer
    x = 1,102.26

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Why These Related Problems?

These problems maintain the same ratio (1.03) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.