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Finding the Third Proportional to 106 and 277.50

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Solution

The third proportional to 106 and 277.50 is: 726.47

Step by Step Solution

  1. Step 1: Write the proportion equation
    106 : 277.50 = 277.50 : x
  2. Step 2: Convert to fraction form
    106/277.50 = 277.50/x
  3. Step 3: Cross multiply
    106x = 277.50 × 277.50
  4. Step 4: Simplify right side
    106x = 77,006.25
  5. Step 5: Solve for x
    x = 77,006.25/106
  6. Step 6: Final answer
    x = 726.47

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Why These Related Problems?

These problems maintain the same ratio (2.62) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.