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Finding the Third Proportional to 314 and 414

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Solution

The third proportional to 314 and 414 is: 545.85

Step by Step Solution

  1. Step 1: Write the proportion equation
    314 : 414 = 414 : x
  2. Step 2: Convert to fraction form
    314/414 = 414/x
  3. Step 3: Cross multiply
    314x = 414 × 414
  4. Step 4: Simplify right side
    314x = 171,396
  5. Step 5: Solve for x
    x = 171,396/314
  6. Step 6: Final answer
    x = 545.85

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These problems maintain the same ratio (1.32) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.