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Finding the Third Proportional to 65 and 69

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Solution

The third proportional to 65 and 69 is: 73.25

Step by Step Solution

  1. Step 1: Write the proportion equation
    65 : 69 = 69 : x
  2. Step 2: Convert to fraction form
    65/69 = 69/x
  3. Step 3: Cross multiply
    65x = 69 × 69
  4. Step 4: Simplify right side
    65x = 4,761
  5. Step 5: Solve for x
    x = 4,761/65
  6. Step 6: Final answer
    x = 73.25

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Why These Related Problems?

These problems maintain the same ratio (1.06) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.