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Finding the Third Proportional to 299 and 410

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Solution

The third proportional to 299 and 410 is: 562.21

Step by Step Solution

  1. Step 1: Write the proportion equation
    299 : 410 = 410 : x
  2. Step 2: Convert to fraction form
    299/410 = 410/x
  3. Step 3: Cross multiply
    299x = 410 × 410
  4. Step 4: Simplify right side
    299x = 168,100
  5. Step 5: Solve for x
    x = 168,100/299
  6. Step 6: Final answer
    x = 562.21

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These problems maintain the same ratio (1.37) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.