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Finding the Third Proportional to 417 and 583.50

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Solution

The third proportional to 417 and 583.50 is: 816.48

Step by Step Solution

  1. Step 1: Write the proportion equation
    417 : 583.50 = 583.50 : x
  2. Step 2: Convert to fraction form
    417/583.50 = 583.50/x
  3. Step 3: Cross multiply
    417x = 583.50 × 583.50
  4. Step 4: Simplify right side
    417x = 340,472.25
  5. Step 5: Solve for x
    x = 340,472.25/417
  6. Step 6: Final answer
    x = 816.48

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Why These Related Problems?

These problems maintain the same ratio (1.40) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.