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Finding the Third Proportional to 410.50 and 769.75

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Solution

The third proportional to 410.50 and 769.75 is: 1,443.40

Step by Step Solution

  1. Step 1: Write the proportion equation
    410.50 : 769.75 = 769.75 : x
  2. Step 2: Convert to fraction form
    410.50/769.75 = 769.75/x
  3. Step 3: Cross multiply
    410.50x = 769.75 × 769.75
  4. Step 4: Simplify right side
    410.50x = 592,515.06
  5. Step 5: Solve for x
    x = 592,515.06/410.50
  6. Step 6: Final answer
    x = 1,443.40

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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.