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Finding the Third Proportional to 106.94 and 233.06

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Solution

The third proportional to 106.94 and 233.06 is: 507.94

Step by Step Solution

  1. Step 1: Write the proportion equation
    106.94 : 233.06 = 233.06 : x
  2. Step 2: Convert to fraction form
    106.94/233.06 = 233.06/x
  3. Step 3: Cross multiply
    106.94x = 233.06 × 233.06
  4. Step 4: Simplify right side
    106.94x = 54,318.13
  5. Step 5: Solve for x
    x = 54,318.13/106.94
  6. Step 6: Final answer
    x = 507.94

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Why These Related Problems?

These problems maintain the same ratio (2.18) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.