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Finding the Third Proportional to 213.50 and 277.50

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Solution

The third proportional to 213.50 and 277.50 is: 360.69

Step by Step Solution

  1. Step 1: Write the proportion equation
    213.50 : 277.50 = 277.50 : x
  2. Step 2: Convert to fraction form
    213.50/277.50 = 277.50/x
  3. Step 3: Cross multiply
    213.50x = 277.50 × 277.50
  4. Step 4: Simplify right side
    213.50x = 77,006.25
  5. Step 5: Solve for x
    x = 77,006.25/213.50
  6. Step 6: Final answer
    x = 360.69

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Why These Related Problems?

These problems maintain the same ratio (1.30) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.