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Finding the Third Proportional to 106.50 and 233.63

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Solution

The third proportional to 106.50 and 233.63 is: 512.49

Step by Step Solution

  1. Step 1: Write the proportion equation
    106.50 : 233.63 = 233.63 : x
  2. Step 2: Convert to fraction form
    106.50/233.63 = 233.63/x
  3. Step 3: Cross multiply
    106.50x = 233.63 × 233.63
  4. Step 4: Simplify right side
    106.50x = 54,580.64
  5. Step 5: Solve for x
    x = 54,580.64/106.50
  6. Step 6: Final answer
    x = 512.49

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Why These Related Problems?

These problems maintain the same ratio (2.19) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.