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Finding the Third Proportional to 65 and 97

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Solution

The third proportional to 65 and 97 is: 144.75

Step by Step Solution

  1. Step 1: Write the proportion equation
    65 : 97 = 97 : x
  2. Step 2: Convert to fraction form
    65/97 = 97/x
  3. Step 3: Cross multiply
    65x = 97 × 97
  4. Step 4: Simplify right side
    65x = 9,409
  5. Step 5: Solve for x
    x = 9,409/65
  6. Step 6: Final answer
    x = 144.75

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Why These Related Problems?

These problems maintain the same ratio (1.49) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.