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Finding the Third Proportional to 128 and 289.25

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Solution

The third proportional to 128 and 289.25 is: 653.64

Step by Step Solution

  1. Step 1: Write the proportion equation
    128 : 289.25 = 289.25 : x
  2. Step 2: Convert to fraction form
    128/289.25 = 289.25/x
  3. Step 3: Cross multiply
    128x = 289.25 × 289.25
  4. Step 4: Simplify right side
    128x = 83,665.56
  5. Step 5: Solve for x
    x = 83,665.56/128
  6. Step 6: Final answer
    x = 653.64

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Why These Related Problems?

These problems maintain the same ratio (2.26) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.