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Finding the Third Proportional to 212.25 and 463.50

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Solution

The third proportional to 212.25 and 463.50 is: 1,012.17

Step by Step Solution

  1. Step 1: Write the proportion equation
    212.25 : 463.50 = 463.50 : x
  2. Step 2: Convert to fraction form
    212.25/463.50 = 463.50/x
  3. Step 3: Cross multiply
    212.25x = 463.50 × 463.50
  4. Step 4: Simplify right side
    212.25x = 214,832.25
  5. Step 5: Solve for x
    x = 214,832.25/212.25
  6. Step 6: Final answer
    x = 1,012.17

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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.