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Finding the Third Proportional to 214.50 and 463.13

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Solution

The third proportional to 214.50 and 463.13 is: 999.93

Step by Step Solution

  1. Step 1: Write the proportion equation
    214.50 : 463.13 = 463.13 : x
  2. Step 2: Convert to fraction form
    214.50/463.13 = 463.13/x
  3. Step 3: Cross multiply
    214.50x = 463.13 × 463.13
  4. Step 4: Simplify right side
    214.50x = 214,484.77
  5. Step 5: Solve for x
    x = 214,484.77/214.50
  6. Step 6: Final answer
    x = 999.93

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Why These Related Problems?

These problems maintain the same ratio (2.16) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.