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Finding the Third Proportional to 857 and 2,024

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Solution

The third proportional to 857 and 2,024 is: 4,780.14

Step by Step Solution

  1. Step 1: Write the proportion equation
    857 : 2,024 = 2,024 : x
  2. Step 2: Convert to fraction form
    857/2,024 = 2,024/x
  3. Step 3: Cross multiply
    857x = 2,024 × 2,024
  4. Step 4: Simplify right side
    857x = 4,096,576
  5. Step 5: Solve for x
    x = 4,096,576/857
  6. Step 6: Final answer
    x = 4,780.14

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Why These Related Problems?

These problems maintain the same ratio (2.36) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.