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Finding the Third Proportional to 42 and 109.75

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Solution

The third proportional to 42 and 109.75 is: 286.79

Step by Step Solution

  1. Step 1: Write the proportion equation
    42 : 109.75 = 109.75 : x
  2. Step 2: Convert to fraction form
    42/109.75 = 109.75/x
  3. Step 3: Cross multiply
    42x = 109.75 × 109.75
  4. Step 4: Simplify right side
    42x = 12,045.06
  5. Step 5: Solve for x
    x = 12,045.06/42
  6. Step 6: Final answer
    x = 286.79

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Why These Related Problems?

These problems maintain the same ratio (2.61) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.