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Finding the Third Proportional to 213.50 and 465.50

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Solution

The third proportional to 213.50 and 465.50 is: 1,014.94

Step by Step Solution

  1. Step 1: Write the proportion equation
    213.50 : 465.50 = 465.50 : x
  2. Step 2: Convert to fraction form
    213.50/465.50 = 465.50/x
  3. Step 3: Cross multiply
    213.50x = 465.50 × 465.50
  4. Step 4: Simplify right side
    213.50x = 216,690.25
  5. Step 5: Solve for x
    x = 216,690.25/213.50
  6. Step 6: Final answer
    x = 1,014.94

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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.