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Finding the Third Proportional to 414 and 776.50

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Solution

The third proportional to 414 and 776.50 is: 1,456.41

Step by Step Solution

  1. Step 1: Write the proportion equation
    414 : 776.50 = 776.50 : x
  2. Step 2: Convert to fraction form
    414/776.50 = 776.50/x
  3. Step 3: Cross multiply
    414x = 776.50 × 776.50
  4. Step 4: Simplify right side
    414x = 602,952.25
  5. Step 5: Solve for x
    x = 602,952.25/414
  6. Step 6: Final answer
    x = 1,456.41

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Why These Related Problems?

These problems maintain the same ratio (1.88) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.