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Finding the Third Proportional to 416 and 1,014

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Solution

The third proportional to 416 and 1,014 is: 2,471.63

Step by Step Solution

  1. Step 1: Write the proportion equation
    416 : 1,014 = 1,014 : x
  2. Step 2: Convert to fraction form
    416/1,014 = 1,014/x
  3. Step 3: Cross multiply
    416x = 1,014 × 1,014
  4. Step 4: Simplify right side
    416x = 1,028,196
  5. Step 5: Solve for x
    x = 1,028,196/416
  6. Step 6: Final answer
    x = 2,471.63

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Why These Related Problems?

These problems maintain the same ratio (2.44) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.