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Finding the Third Proportional to 410 and 686

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Solution

The third proportional to 410 and 686 is: 1,147.80

Step by Step Solution

  1. Step 1: Write the proportion equation
    410 : 686 = 686 : x
  2. Step 2: Convert to fraction form
    410/686 = 686/x
  3. Step 3: Cross multiply
    410x = 686 × 686
  4. Step 4: Simplify right side
    410x = 470,596
  5. Step 5: Solve for x
    x = 470,596/410
  6. Step 6: Final answer
    x = 1,147.80

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These problems maintain the same ratio (1.67) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.