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Finding the Third Proportional to 414 and 442.50

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Solution

The third proportional to 414 and 442.50 is: 472.96

Step by Step Solution

  1. Step 1: Write the proportion equation
    414 : 442.50 = 442.50 : x
  2. Step 2: Convert to fraction form
    414/442.50 = 442.50/x
  3. Step 3: Cross multiply
    414x = 442.50 × 442.50
  4. Step 4: Simplify right side
    414x = 195,806.25
  5. Step 5: Solve for x
    x = 195,806.25/414
  6. Step 6: Final answer
    x = 472.96

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Why These Related Problems?

These problems maintain the same ratio (1.07) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.