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Finding the Third Proportional to 411 and 657.75

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Solution

The third proportional to 411 and 657.75 is: 1,052.64

Step by Step Solution

  1. Step 1: Write the proportion equation
    411 : 657.75 = 657.75 : x
  2. Step 2: Convert to fraction form
    411/657.75 = 657.75/x
  3. Step 3: Cross multiply
    411x = 657.75 × 657.75
  4. Step 4: Simplify right side
    411x = 432,635.06
  5. Step 5: Solve for x
    x = 432,635.06/411
  6. Step 6: Final answer
    x = 1,052.64

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Why These Related Problems?

These problems maintain the same ratio (1.60) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.