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Finding the Third Proportional to 9,857 and 21,541

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Solution

The third proportional to 9,857 and 21,541 is: 47,074.64

Step by Step Solution

  1. Step 1: Write the proportion equation
    9,857 : 21,541 = 21,541 : x
  2. Step 2: Convert to fraction form
    9,857/21,541 = 21,541/x
  3. Step 3: Cross multiply
    9,857x = 21,541 × 21,541
  4. Step 4: Simplify right side
    9,857x = 464,014,681
  5. Step 5: Solve for x
    x = 464,014,681/9,857
  6. Step 6: Final answer
    x = 47,074.64

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Why These Related Problems?

These problems maintain the same ratio (2.19) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.