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Finding the Third Proportional to 414 and 570

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Solution

The third proportional to 414 and 570 is: 784.78

Step by Step Solution

  1. Step 1: Write the proportion equation
    414 : 570 = 570 : x
  2. Step 2: Convert to fraction form
    414/570 = 570/x
  3. Step 3: Cross multiply
    414x = 570 × 570
  4. Step 4: Simplify right side
    414x = 324,900
  5. Step 5: Solve for x
    x = 324,900/414
  6. Step 6: Final answer
    x = 784.78

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These problems maintain the same ratio (1.38) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.