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Finding the Third Proportional to 411.19 and 997.50

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Solution

The third proportional to 411.19 and 997.50 is: 2,419.84

Step by Step Solution

  1. Step 1: Write the proportion equation
    411.19 : 997.50 = 997.50 : x
  2. Step 2: Convert to fraction form
    411.19/997.50 = 997.50/x
  3. Step 3: Cross multiply
    411.19x = 997.50 × 997.50
  4. Step 4: Simplify right side
    411.19x = 995,006.25
  5. Step 5: Solve for x
    x = 995,006.25/411.19
  6. Step 6: Final answer
    x = 2,419.84

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Why These Related Problems?

These problems maintain the same ratio (2.43) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.