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Finding the Third Proportional to 411.80 and 647.21

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Solution

The third proportional to 411.80 and 647.21 is: 1,017.18

Step by Step Solution

  1. Step 1: Write the proportion equation
    411.80 : 647.21 = 647.21 : x
  2. Step 2: Convert to fraction form
    411.80/647.21 = 647.21/x
  3. Step 3: Cross multiply
    411.80x = 647.21 × 647.21
  4. Step 4: Simplify right side
    411.80x = 418,879.47
  5. Step 5: Solve for x
    x = 418,879.47/411.80
  6. Step 6: Final answer
    x = 1,017.18

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Why These Related Problems?

These problems maintain the same ratio (1.57) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.