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Finding the Third Proportional to 410 and 694.50

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Solution

The third proportional to 410 and 694.50 is: 1,176.42

Step by Step Solution

  1. Step 1: Write the proportion equation
    410 : 694.50 = 694.50 : x
  2. Step 2: Convert to fraction form
    410/694.50 = 694.50/x
  3. Step 3: Cross multiply
    410x = 694.50 × 694.50
  4. Step 4: Simplify right side
    410x = 482,330.25
  5. Step 5: Solve for x
    x = 482,330.25/410
  6. Step 6: Final answer
    x = 1,176.42

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Why These Related Problems?

These problems maintain the same ratio (1.69) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.