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Finding the Third Proportional to 214 and 420

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Solution

The third proportional to 214 and 420 is: 824.30

Step by Step Solution

  1. Step 1: Write the proportion equation
    214 : 420 = 420 : x
  2. Step 2: Convert to fraction form
    214/420 = 420/x
  3. Step 3: Cross multiply
    214x = 420 × 420
  4. Step 4: Simplify right side
    214x = 176,400
  5. Step 5: Solve for x
    x = 176,400/214
  6. Step 6: Final answer
    x = 824.30

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Why These Related Problems?

These problems maintain the same ratio (1.96) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.